Ok first I'll be fair, in regards to her and the akatsuki:
Pain>Tsunade
Sasori and Tsunade can go either way but I give it to Tsunade, because her reflexes are of course better than Sakura si she won't be needing any puppet strings and if she had the chance to make anti-poison like Sakura she has a chance of winning.
Kakuzu and Tsunade could also go either way, but I'm giving it to Kakuzu.
Hidan and Tsunade I give this to Tsunade if she has knowledge beforehand.
Konan and Tsunade I give this to Tsunade
Tobi>Tsunade
Itachi>Tsunade
Deidara>Tsunade the fact that he is up in the air while she runs straight to all her opponent is just lol
Tsunade>Zetsu
Now in terms of her being the best Hokage for administration I think some of you are mistaken; in term of the ruling aspect
Hashirama: A warrior Hokage that fights all his life and create the country-
Tobirama: A visionary Hokage that created the Chuunin Stadium, anbu black OPS and Uchiha Police he was the Hokage that gave life to Konoha's system a person like this requires Vision
Sarutobi: A peace Hokage that served the longest and led the people to a path of peace
Minato: We know too less about him, but to be able to become Hokage at his age one can imagine what sort of man he was.
Now Tsunade, we know of one thing she created the medical system of Konoha while great what does that reference to? 'Head of a Hospital'. This is one reason why people choose not to acknowledge her. She was never considered for the Hokage position by previous Hokages and not even the elders had her in mind until they ran out of options. Someone mentioned she was quick to react but how does this surpass the other hokages, Hashirama for one fought in battle all his life until his final few years. You mean he wasn't quick to react to problems?
Now on to her skills
Its fine you all think she is a great support medical ninja and have great brute strength but the reason people hate her also comes from here, an example is during the Madara vs 5Kage fight- when Madara used the Flowerpath or tree path, (I can't remember) instead of doing her job finding a solution to the pollen or warning them about its effect her words were "that's grandfather's" and then fainted soon after I can imagine A a taijutsu fighter falling so fast but it just sent her knocking -_- and she would've died if not for Oonoki.
During the Pain arc- her actions were just plain stupid no matter how majestic you guys think it was- while Pain destroys everything and the people she was just conducting her healing jutsu on them- now the wisest action would've been to come up to Pain n prevent him from killing anymore while getting the Anbus to take everyone to a different place- basically her strategy was keep killing I'll just keep healing I won't stop u and when I'm out of chakra and u confront me I'll run my mouth of.
Raising Disciple- Hashirama/Tobirama trained Sarutobi/Danzo light and shadow of the leaf, Sarutobi trained 3 Sannins,
Orochimaru trained: Sasuke: Avenger that seeks to destroy the leaf/killed Danzo,Deidara and destroyed Oro's ambition/ stormed the kage submit and screwed A's arm.
Kabuto: Surpassed Orochimaru, mind fked Tobi with real Madara, one of the key players in the 4th Shinobi War
Anko: Funky Dango lover you can't argue with that.
Since this is getting quite big I won't talk about Jiraiya which you guys obviously know.
Finally we have Tsunade:
Shizune: became a support character with a smaller impact than TonTon long ago
Sakura: An epic Main character that has.......... NO use
And finally her healing is still far away from Hashirama- her mitotic has a bad side effect and it decreases her life span.
With all that said that's my point on why some people including myself not acknowledge her, while I admit she is pretty cool and 10times better than Sakura