Alright, let's get my criticism out of the way first. Props for the time and effort this obviously took to put together, you have clearly thought this one through. That being said, for such a giant clash of shinobi, I think it may have been easier to do in parts and then just tally the score later (that being each fight a different thread) but nonetheless still an interesting battle.
As for the battle itself, as others have said it is a little bit more than bias that you picked most of match-ups in the Akatsuki's favor. Also, who's to say they would even fight them in a duel setting? We have been reading a pretty long team battle involving the current Kage and if anything it really showcases teamwork, which in my opinion we've been missing a lot of since part 1. That being said, I don't necessarily believe the Kage would be a better team, it's just a good idea to keep in mind that some of these characters would make excellent teammates with one another and could turn the tide with some clever strategy or combination jutsu.
If I have any other criticism it is that I don't really like judging fights with characters that have limited information, especially when people make very large and unwarranted claims of their power. Like the third Kazekage who has had absolutely no appearance or information other than he used iron sand.
On to the matchups, all my notes are brief due to the sheer number of characters:
-1) Itachi vs Second Tsuchikage
This fight comes down to one major factor, can the Tsuchikage use his invisibility effectively. This is a very argumentative because we simply don't know how his ability works. What we do know though, is that another shinobi has used a similar technique and was easily discovered by a novice sharingan user. Obviously the scale between these characters is great but the principle remains the same. It is of my opinion that Itachi could detect the Tsuchikage with his sharingan.
So, unless the Tsuchikage can ambush Itachi while his sharingan is inactive -- I give this match to Itachi because of his powerful techs and intelligence to use them effectively.
-2) Kisame vs Second Hokage
Kisame was born to fight this Hokage, I mean like really. Let's skip right past the nonsense about his space-time and edo techniques since we know jack squat about them. They are in no way comparable to what Minato, Orochimaru or Kabuto have done respectively so don't even try mentioning them. If the Second was honestly capable of that type of power he wouldn't have died in battle, especially in such a lame way as he did.
So, if we assume he doesn't teleport around crazily and he can't mass an army of the dead we are left with... water, lots and lots of water. Who enjoys a water-filled battlefield? SHARKMAN, that's who. -- But in all seriousness, Kisame has proved to have some of the best if not strongest water techs in the series. Combine that with chakra sucking, shark-mode and his already massive chakra supply and he just seems like a better, stronger water user. Kisame wins.
-3) Hidan vs Fifth Mizukage
I always laugh at Hidan, he was the worse joke the Akatsuki had to offer. Any and all fights with him come down to two parts: is he capable of damaging his opponent and is his opponent dumb enough to let him do so?
Fifth Mizukage is a mid to long range combatant with some powerful techniques. Techniques in fact that might actually be capable of killing the so called "immortal". Let's face it, we've clearly seen that you can cut up Hidan in chunks and leave him to rot for all eternity. Who's to say he can't be melted down into nothingness? Or simply obliterated by an even greater attack? Nothing. Nothing says he can't be simply erased, he just can't die by hitting what is normally a vital spot, organ or otherwise.
So, the Mizukage has the arsenal to potentially send him to his final grave the question remains if she is dumb enough to get hit by him and then inevitable ritualized. The answer is a toss-up, I'm afraid. She has shown to be hot tempered and quick to act, but that doesn't necessarily mean she will catch him in her ninjutsu right-away. I could see a situation where he walks through the corrosive mist just to cut her head off as she stares in shock. Bottom line, I call this a 50/50.
-4) Deidara vs Fourth Hokage
Deidara has to the tools to win but he won't, sorry. The Fourth specializes in having a quick decisive answer to every opponent. I believe this to be the type of fight where the opponent is defeated before he even thinks of using his more powerful techs, simply because he underestimates his opponent and gets blitzed early on.
As for Minato, he has a counter to the C0 and all other C's in two abilities: Flying Thunder God and Space-Time Barrier. He could avoid or redirect the attacks, so long as he knew how. C4 could be his downfall, although I'm confident he could avoid it with space-time, he has to know it's danger and range to do so effectively, hard to figure out without knowledge or dojutsu. Still, I think it won't come to that. I give this to Minato 9 times out of 10.
-5) Kakuzu vs Second Mizukage
I don't like neither of these guys to be honest. I think they both have some powerful techniques and the fight could go either way. The second would probably get the first hint of victory but may then subsequently be surprised by the fact that he has to kill him several more times to actually win. Giving it a 50/50 mostly because I don't want to think about this match-up extensively. If I had to lean one way, I'd say Kakuzu just because he takes battles more seriously and seems to think ahead.
-6) Sasori vs Third Kazekage
This is perhaps the worst part of this list, putting up a Kage who has no real feats or appearance in the manga against a guy who already beat him once? It's not really fair, Sasori wins this by default but I certainly don't agree with the match-up.
-7) Zetsu vs Fifth Kazekage
Gaara > Fodder. No but seriously, until we see a super Zetsu or something Gaara takes this one easily. Zetsu has been defeated by chuunin level shinobi all war.
-8) Nagato vs Third Hokage
Nagato wins this until we see what Prime Hiruzen is capable of.
-9) Konan vs Third Tsuchikage
The Third Tsuchikage takes this with some difficulty. The only way I could see Konan winning is if she used her massive paper-bomb trap. Which in my opinion requires too much set-up and is way too situational to count. Tsuchikage wins in every battlefield other than Konan's home base.
-10)Tobi vs Third Raikage
Uhm, what? Is this Madara-Tobi or Deidara's Tobi? I mean, it's an absolute overkill if it's the Tobi with rinnegan. Assuming it's the simplified Tobi, it's still debatable. I mean, he is practically invulnerable and he can simply warp his opponent to his own space. Yeah, I'd lean towards Tobi simply because the Raikage are notorious brutes with little to no battle tactics.
I spent way longer on this than I intended, not as brief as I wanted to be. Anyway, if we tally the score it's something like: Akatsuki 5, Kage 3 and two undecided (fights 3 and 5). So while it may look like Akatsuki win, this score is 5 to 3 in a scenario that heavily favors the Akatsuki. So take from that what you will.