So first of all let me start by saying that before I joined this forum I never even thought Hiruzen is all that. I knew he was good (he was Hokage so of course he was reallt good) but I never saw him as top 10 or even 20 material. However for some reason people at NB seem to think he is like God tier or something. At first I thought it was a joke but no people actually believe he is greater than Madara, Nagato, Itachi, Sasuke, Minato and even So6P (no joke

). I've even some people think he could've stopped tobi the day the nine tails attacked. I just can't understand it. I personally feel Guy would take him, I mean this isn't part 1 anymore, so many shinobi have surpassed him IMO.
Anyway just needed to get that out of the way, now back on topic. Now before any fan boys start, I'm referring to the Hiruzen we have all seen fight, not prime, not hype cuz as far as I'm concerned that Hiruzen doesn't exist. Oh what the hell, so hiruzen fan boys don't cry you can use prime hiruzen if you want. I still don't see how Kakashi will lose.
In part 1 Hiruzen would have taken down Kakashi for sure, low-mid diff. But now from what I've seen from current kakashi I don't think its possible. Hiruzen uses fire and earth style jutsu, kakashi also uses earth and fire (I think). Even if kakashi doesn't technically have fire he has powerful water jutsu that can counter hiruzen's fire jutsu. Kakashi used lightning which also overcomes hiruzens earth. Some may say but "oh, hiruzen has mastered all jutsu of hidden leaf, so what - kakashi has over 1000 jutsu copied world wide. So in terms of ninjutsu kakashi clearly wins right.
Hiruzen was called the professer so I'm guessing he's incredibly smart, same goes for kakashi since he's regarded as a genius. From what I've seen Kakshi has more tactical strategic thinking in battle. Hiruzen may have more intellegence but I feel kakashi would outsmart him in a fight.
In terms of speed, you have to be stupid to say Hiruzen, I doubt prime hiruzen is faster than kakashi either. No matter how fast hiruzen may have been, kakashi's sharingan will always give him the advantage since he can read any of hiruzens movements.
I don't even think Kakashi needs Kamui to win this, Kakashi's abilities olone suggest to me that he would win in a battle to the death.
This is just my thoughts though, feel free to tell me otherwise but no fanboyish arguments such as because hiruzen is god of shinobi he will win (BS!!).