Who is the numero uno 1v1 Champ of the league?

[Tyr]

Why has no one mentioned Jax?

Jax can easily beat Tryn.

Sword of the Divine just solves the problem all too easily if they're all decked out. If Tryndamere gets all those attacks up (say Jax jumped and initiated on Trynd) he'll probably swiftly get floored if Trynd just gets a little lucky with crits.

I mean it really all depends on item builds but I believe in a game where they both started 1v1 (knowing the opponent from get go), get 6 item'd, I believe Tryndamere would probably end just about 95% of all the champions. There lacks crowd control items for them to be able to tame Tryndamere with the new ("old)" cleanse and the quicksilver sash.