Lets assess the situation.
First off, both Tsunade and Kakashi were seen as protegees in their own right, each making up for something the other may lack while being on par in most fields battle.
Tsunade is naturally more physically capable of higher level combat as her Senju ties grant her longevity, natural strength, deeper chakra reserves, and amazing tenacity. She excels naturally in chakra control being able to utilize her chakra in almost any region of her body with such precision unique precision. Her predetermined greatness is shadowed by the lack of various Ninjutsu that she may or may not utilize in battle, but her experience and extensive knowledge of various techniques, and not to mention various ninja in the village from her position as Hokage (among those would be Kakashi of course). What she lacks in quantity of Ninjutsu, she gains in quality of jutsu. Her application of medical knowledge boosts her base strength to monstrously devastating levels while notably being able to heal herself from the most fatal of injuries without the use of hand seals. This builds an array of new techniques not easily distinguished from standard elemental Ninjutsu.
Kakashi has gained,through training, an array of ninjutsu, keen intelligence, and a vast amount of experience at a young age. Kakashi initially struggled with slightly above average chakra reserves, has compensated for this with the same or even greater precision in chakra control in the utilization of his arsenal of techniques which is even further expanded with the addition of his Sharingan which has also contributed to the increase in his chakra reserves. Kakashi may be of average build for a Jonin of the time, but his extensive intelligence and experience in Ninjutsu makes up for the lack of a physical advantage (other than his Sharingan obviously). The advantages he receives from sharangan allows him to read© most techniques&in its advanced Mangekyu are devastating Space-Time Ninjutsu Kamui. These combined attributes easily put him as a candidate for the Hokage, putting him at least on par with Tsunade (being relatively from the same time or occurring around the same time *we know.Tsunade is old*)
Now I could continue to magnify the attributes each one has but lets start looking at them together in comparison.
Ninjutsu:
Kakashi:- would have a great advantage here being able to manipulate an array of jutsus to throw Tsunade for a loop and even wear her down with physical damage and thus forcing her to heal her injuries, that is if he is able to hit her.
Tsunade:- would be at a lesser advantage because her fighting style revolves around the application of Medical ninjutsu, but one culd call this an advantage over someone who has no knowledge of the matter.
So: Kakashi may be able to barrage Tsunade, but she is capable of avoiding him and may in turn take her chances of being hit if the situation calls for it and likely survive the barrage. Leaving both shinobi in a worn down state.
Taijutsu:
Heres the tough one.
Kakashi:- is a more than capable of handling himself against skilled taijutsu users, often using clones or substitution to assess the opponents with his sharingan while avoiding damage and keeping the enemy at bay. However, his experience in taijutsu is not that of Tsunade.
Tsunade:- may have difficulty trying to hit someone with her taijutsu, but is much more adept at using her physical power and has therefore developed an unsurpassed form of hand to hand combat as it centers around not taking even the slightest scratch. One hit from her and Kakashi may be in trouble, with no backup to heal him.
So: This is all dependant on who lands the first blow. Likely Tsunade will take the offensive having known Kakashi&if Kakashi is able to avoid Tsunade long enough to read through her movements and counter he could take the advantage. If he is hit by Tsunade once however, he is at a great disadvantage.
Genjutsu:
Tsunade:- has shown some knowledge of Genjutsu (ex. filler w/ Legendary Stupid Brothers "Genjutsu: Binding") and even the human psyche being able to completely reverse the effects of Tsukuyomi (the strongest of genjutsu btw) on Kakashi&Sasuke. She herself has rarely used genjutsu, but probably has a knowledge of it.
Kakashi:- also a rare genjutsu user, is capable of dispelling the most powerful of genjutsu and/or at least withstand them. The addition of his Sharingan he is able to subdue almost any opponent in a genjutsu of standard "Sharingan proportions".
Since both of them hardly uses genjutsu, and both probably know the capabilities of the other in this particular field, its safe to say they wont be resorting to this any time soon.
Intelligence:
Kakashi:- is calm, witty and deductive in the highest sense. He is proven to be more than intelligent enough to see through incoming danger of the widest variety, and come up with resourceful solutions in almsot an instant. His experience in the Anbu Black Ops has shot his experience as a team leader to tremendous heights, however teams aren't used in a duel. Still he is capable of handling an opponent on his own with his own precautions.
Tsunade:- appears to be short tempered, but has proven to be a more than capable leader achieving the rank of a Kage. She is a keen thinker, being highly observant and analytical to the point of seeing through most deceptions, rarely being caught off guard. She is capable of assembling the optimum team to cary out missions, yet teams are not used in duels. Among her knowledge of almost every record in the Hidden Leaf Archives, she carries the base and full understanding of medical ninjutsu. Having created the system herself, her knowledge of the matter allows her to diagnose ailments with a glance, and tactfully counter attacks of this nature.
So: The fact of the matter is, they are both equally intelligent. If they weren't at least equals in mentality, neither of them would have been even considered for the roll of Hokage. Tsunade may have the advantage, having the knowledge of Kakashi and his current stats being his senior and having an arsenal that Kakashi is not completely versed in: Medical Ninjutsu.Kakashi may have to take the time to read Tsunade before he makes a decisive move, all the while Tsunade knowing this will be his strength with his Sharingan They aren't oblivious of one another, so it would be a tough to say that Tsunade would be so easily caught by Kakashi or vice versa.
Strength:
Kakashi:- has shown a basic form of strength, having studied Might Guys fighting style throughout the years, and incorporating the Strong Fist's strength into his Taijutsu. His blows are direct and powerful.
Tsunade:- was born with natural tremendous raw physical strength through the Senju clan. She has taken this strength to new levels with the use of Medical Ninjutsu, expelling chakra at the precise point of impact granting her monstrous strength enoughh to demolish any object from her feet all the way to the tip of her finger.
So: This is obviously where Kakashi pales in comparison to Tsunade. Kakashi can easily compensate for this disadvantage by simply avoiding Tsunade's blows, but Tsunade has increased her arsenal of natural tools (earth, rock, tree, even giant blades if available) that she could use to her advantage being far less predictable than elemental ninjutsu, yet easily readable via the Sharingan through its basic linear styles.
Speed:
Kakashi:- is quick and evasive, even in the tightest of situations, being able to avoid various elemental techniques. With the aid of his Sharingan he is able to quickly assess a situation and react accordingly, while this may drain his chakra, he has shown to be proficient enough to use it for almost an entire day.
Tsunade:- has based her entire medical philosophy on a few rules, one of the primary being to avoid being hurt or captured first and foremost, which she herself has proven to easily be able avoid serious injury when needed. With the use of her Chakra Enhanced Strength, she can propel herself quickly in any one direction either to avoid attack, or to embrace an attack for another if necessary. She has practiced the art of avoidance and has drilled these rituals into her pupils Sakura and Shizune.
So: Kakashi may be a little bit swifter and nimbler which would give him an advantage over Tsunade and her linear attacks, regardless of her speed, however, it is still possible that Tsunade could keep away from Kakashi on the defensive.
Stamina:
This is also a point of conflict.
Kakashi:- as previously stated has built his chakra to a substantial level being able to use his Lightning Blade technique at least 6 times and Kamui at least 4 times before becoming fatiuged. His precice control of the use of his chakra plays more of an influential role in his stamina rather than his chakra reserves as he is able to use a vast many jutsu in quick sucession but requires a replenishing or recovery session periodically to replenish chakra.
Tsunade:- was gifted with substantial chakra reserves allowing her to use numerous techniques as well but also lets her use and maintain multiple abilities at the same, without becoming entirely fatiuged allowing her to maintain extreme combat for extended lengths of time. Her control allows her to use techniques to their fullest extent without wasted chakra or timing.
So: Kakashi may have a newly deepened chakra reservoir granting him a longer battle ability, it cant compare to the amount of chakra that Tsunade has been innately gifted, along with her reserve seal placed on her forehead for emergency situations to facilitate the use of her powerful recovery techniques.
Hand Seals:
Simple
Kakashi:- is probably swifter and well versed and practiced in many techniques.
Tsunade:- May have knowledge of techniques, but does not practice them, therefore may be slower.
So: However Kakashi has become swift in his sign usage so as not to need them entirely, while Tsunade in the same right hardly uses hand seals herself but neither is less knowledgeable than the other.
To Me:
It appears that neither victory would be an easy one for either shinobi. They both have extensive experience in Taijutsu and leadership tactics, making their individual decision making and analysis strong in itself. They are both capable of keeping up with one another and cunning enough to keep the other on their toes for any amount of time. While Kakashi has an arsenal of deadly Ninjutsu, he isn't stupid enough to resort to his most taxing jutsu immediately simply to eliminate his opponent quickly, for he knows Tsunade knows well of his abilities and has probably considered this tactic long before the battle began. Who is to say she can't unearth large enough rocks with a single punch instantaneously with enough time to be absorbed by Kamui which takes at least a moment to prepare as well. We know Kakashi has evolved his use in the Sharingan, however we must remember he is still not of Uchiha blood, making his excelled use an extraordinary feat, but not to the precision of an Uchiha member and is somewhat limited, even slightly. If he were to wear her down with his elemental ninjutsu he may have an opportunity to injure Tsunade even greatly from such moves as the Lightning Blade. Tsunade however appears to have the tenacity and durability to live through such a fatal injury while also providing a swift and powerful counterattack if her opponent is in range. Likely Kakashi would have ruled out this approach and kept a barrage from affar using his various long range Ninjutsu, which may provide Tsunade an opportunity to evade his long range barrage. To compensate Kakashi might summon his ninja hounds to distract or aide him, to which either Tsunade could physically/medically harm them herself or counteract by summoning Katsuyu who can either shield her or multiply to assist. Being a much larger summon id imagine she would be stronger than the ninja hounds, but i cant really say (i havent researched them enough, sorry). If Kakashi manages to hit Tsunade first, id imagine that he would end up being the first to land a blow either because he caught Tsunade himself, but in probability, Tsunade allowed herself to become hit by a technique she could survive just to get closer to Kakashi. This could happen numerous times either in quick succession or in spurts, but this rapid healing by Tsunade is ever draining her chakra, while Kakashi is being drained from attacking in quick succession. I wouldnt put it past Kakashi to already see through Tsunade's "powerhouse barrage" and probably prepared a substitution of some sort in case she did catch him, to which Tsunade would make sure she would catch him no matter what. If Kakashi fools Tsunade with this ruse&is able to continue using chakra there may be a chance to hit her possibly from underground, but clever Tsunade probably though this as well or maybe even saw it happen and simply evades or worse strikes the ground beneath her before he has the opportunity to counter. Lets say the latter happens (since we probably know she can dodge underground attacks from her fight with Kabuto), but it only unearths Kakashi without injury, both have probably expended a good portion of their chakra&may take this revealing to attack one another. This could either be a trap on either end or a stalemate depending on the approach taken. They continue to test each other toe to toe until a point of recovery. Tsunade will probably have the upperhand in this case, being able to heal ailments and regain more stamina than Kakashi at the cost of her chakra, while Kakashi may be prepared for another full barrage. Ultimately it comes to who takes down who the fastest because Tsunade will likely outlast Kakashi.
I would call this a draw because i doubt Kakashi could actually kill Tsunade because of her healing techniques, yet Tsunade wouldnt have the extra chakra to finish Kakashi after defending from him.
Hows that?