There's NOT a best 1v1 champ - I'll throw out a perfect example, who would in Cait vs. Rammus? I think if you asked a lot of really good players you'd get a ton of different answers - the best cait might able to beat the worst rammus, but the best rammus might be able to beat the worst cait.
It comes down to how well you understand the mechanics of the current champion you're playing, and how they work together or against the champ you are 1v1 against. The champion's ability is limited only by the ability of the person controlling it.
I see Warwick up there - if someone is playing WW, and they have played about 20 games with him. Even if he fights an Eve 1v1, if the person playing Eve has let's say 50 games with WW - I think the Eve will win against her WW opponent because they have a more thorough understanding of how that champion works, and as a result can counter him more effectively. Especially if you're opponent has never played the champion he's against himself lol.
Know your opponent, better than he knows himself - and you will be met with victory 90% of the time in any matchup 1v1, or at least not die lol.