@Scottrf: Well, I thought it was clear in my post. I was talking about Kramnik at his best playing stronger than Carlsen at his best. I'm talking about their actual strength at their "peak" performance. Who's better at sustaining a reasonably high level of performance over the course of a tournament is obviously a completely different question.
I don't know what you mean by "flawless." He's played a lot of games that are very impressive, for sure. But I think Kramnik's trademark is just to create games that are almost like lessons -- where he finds some opening novelty that creates some quirk in the position -- some sort of fixed color complex or a passed pawn. And he just methodically milks that advantage with these deceptively simple moves, which when you run it through a computer, rely on critical lines that are many moves deep. And then he cashes it out in some winning (albeit difficult) endgame, which he plays perfectly, and the whole thing feels like it's like a composition from beginning to end.
Carlsen's best games feel more like Karpov (also a favorite of mine). He just nudges and nudges and doesn't make mistakes, and eventually he nudges his opponent until he runs out of good moves, or makes a small mistake, upon which Carlsen can pounce. I think that's a very good practical way of playing. With a few notable exceptions, I think the players with the best tournament results tend to play like that. But I think when matched up against Kramnik in top form, Carlsen's nudge approach isn't effective.
I guess this sort of makes sense. To play like Kramnik in top form, I imagine, requires enormous amounts of energy. Carlsen gets excellent results expending considerably less energy, so overall, it's probably a better way of approaching the game. And I suppose the results bear that out.
As for "proving" it -- it's a subjective assessment. I never really understood why people were always demanding proofs for every claim. Outside of mathematics and logic, you can't ever "prove" anything. All you can do is provide evidence. And when it comes to something like estimating how strong a chess player is at his best -- it's really not easy to provide evidence. It's a subjective evaluation.
I also think that Federer at his best is better than Nadal at his best, even though their head-to-head is WAY in Nadal's favor. I just think that Nadal almost always plays at or near his peak, whereas Federer is prone to dips in concentration. Also, there are other factors like surface and playing style, but this isn't a tennis forum, so I won't get into those details. The point is that the abstract notion of a player's "best," is something that's not easy to measure. Maybe there's some way to be more formal about it by running games through chess engines, but I doubt that's entirely conclusive.
Daniel, I think your comments are very insightful. Thank you!
Is that because Hikaru Nakamura is a St Louis Blues ice hockey fan?
Or is it because Hikaru Nakamura is ethnically Japanese and loyally American?
CorfitzUlfeldt, What is your answer?
Neither. It has more to do with him comming across as slightly douchey.
I see.
So you're more of a fan of the Tampax Bay Lightning?