better player

I'd say Kasparov because even though he hasn't played top level for awhile, Fischer is at a bigger disadvantage, being dead and all.

Fischer was an Aspergian(Form of autism), Kasparov wasn't...Fischer Wins

If I've said it once, I've said it a million times, knights taste better than bishops, and Fischer looks better in a jacket than Kasparov.

I was at the Las Vegas International Chess festival for the 2012 National Open, there I met IGM Anatoli Karpov. A question was asked, "who was the best chess player?". GM Karpov replied with "you can't say... Paul Murphy was the best of his time; Its different times". I agree with his answer. In regards to Fischer and Kasparov question this same idea applies. There is no Kasparov without Fischer. Kasparov grew from Fischer's ideas... that's why they almost have the same playing style- King's Indian and Najdorf player. By the same token there is no Fischer without the Russian School System of Botvinnik.

I guess the question must be broaden to "what challenges made these great persons the best?" and in that regard Robert James Fischer the 11th world Champion REIGN SUPREME... he was 1 against the world in his way to the top!!!!

i think kasparov is better

To me Kasparov is better than Fischer, but Alekhine is the best overall.