why not ask Kasparov?
Fischer vs. Kasparov

Not sure if we can claim that Fischer had photographic memory.
According to this:
http://www.guardian.co.uk/obituaries/story/0,,2243089,00.html
"During Leipzig I also gave the top grandmasters memory tests for the BBC programme, with revealing results. Tal, prompted with some obscure game, rattled off the opening and the occasion, and when it was his own game, gave me a resume of the pre-game banter and the post-mortem analysis. Fischer's memory, by contrast, was excellent only for his own wins."
The current view by psychologists is that there isn't such a thing as photographic memory. It's just a well preserved urban myth. There are however some individuals - mostly prestigious savants - who are able to hold highly detailed and complex after-images of a scene (eidetic memory), but even these are prone to subjective distortion.

I have an eidetic memory - could never understand why so many people seemed comfortable with lying till I studied psychology and discovered that it a memory problem rather than a moral deficiency - changed my whole outlook on humanity in general

Fischer an later Kasparov were the most charismatic chess players ever. No one has ever contributed to the popularity of chess more then these two giants, each in his own time. Pele or Maradona?
I think comparing chess players from different eras is fun but pointless simply because of the analysis advantage the more modern player has. However over the board I believe fischer was better and more talented.

I would say that Kasparov would beat Fischer if they both fought it out at both of their successful peaks. However, I believe that Fischer would have been better than him if he had all the resources that are available to chess players now. He studied alone and read hundreds of books on his free time. Kasparov and most other GMs had tutelage from other masters. Yet, even as a lone wolf, Fischer dominated.
Fischer won his impressive matches in 1971 and 1972 without any help, while the soviet players had grandmasters analyzing the games for them. He would have swept the floor with Karpov who narrowly has beaten Korchnoi in the seventies, Korchnoi, who never made it in a WC-Final before. And Fischer also ( in his prime) is stronger than Kasparov, who was better than Karpow by a small margin only. In 1971, Fischer beat the world No. 9 and the world No. 3 both 6-0!! Petrosjan, only three years after he has been world champion, was beaten 5-1.

The indisputable answer is that Fischov would have won, but Kasparer would have kept it a close match.

I believe that Fischer at his peak is better than Kasparov at his peak, but there is little doubt that in 1992 Kasparov was better. I personally think Fischer was pretty much burned out after the 1972 match with Spassky and would have lost to Karpov if he had played him after that.

If Mikhail Tal had stopped playing chess in 1961, we could easily speculate, based on his results at his 1959-1961 peak, that he would have won against Fischer in 1971. However, he kept playing and so we happen to know that his subsequent results were not anywhere near those at his peak. This is due to a variety of reasons such as his poor health, opponents adapting to his style, new top players coming in, his less than perfect working habits etc. There is no guarantee that, if Fischer kept playing, he would have simply maintained his peak strength / results. As his breakdown suggests, that peak might not have been humanly maintainable for a prolonger period of time.

Kasparov would win. Fischer never played seriously after 1972. Chess theory exploded after Fischer - Spassky. Kasparov benfitted from that. Fischer did not. They are players of different eras.
Fischer was great, but his personal demons grew from distracting his opponents to destroying his career and his life. Admire his talent, but pity the man.
If Fischer and Kasparov were the same age and competed during the 1960-1972 timeline, I'd say Fischer would definately be much better.
If they were the same age and competed between the 1985-2000 timeline, hard to say but I'd lean toward Kasparov, because Fischer seems to hate computers which would be a big disadvantage.
If 1972 Fischer competed against 1999 Kasparov, I'd say Kasparov wins because he already reaped the developments and theory that Fischer helped develop, and has his massive computer opening databases to back him up.
Overall I'd say Fischer was better though, because he had to learn a little Russian to read the best Chess books, find and collect the right books on various theory, write down notes manually, do variations over the board instead of clicking through them real quick, etc.

Overall I'd say Fischer was better though, because he had to learn a little Russian to read the best Chess books, find and collect the right books on various theory, write down notes manually, do variations over the board instead of clicking through them real quick, etc.
Lol Kasparov speaks Russian and English doesn't he ?
Overall I'd say Fischer was better though, because he had to learn a little Russian to read the best Chess books, find and collect the right books on various theory, write down notes manually, do variations over the board instead of clicking through them real quick, etc.
Lol Kasparov speaks Russian and English doesn't he ?
Kasparov didn't learn English to read English Chess books. Fischer was singularly interested in Chess, not the Russian language, he just learned it to read their chess literature.
But Fischer was American. We all know Americans are better than everyone else. So when an American learns a foreign language, he gets extra credit. Even if Kasparov can communicate in Spanish, French, German, Russian and English, he's not as good as an American who learned enough Russian to read a chess article.
I disagree, and that's pretty racist.

Overall I'd say Fischer was better though, because he had to learn a little Russian to read the best Chess books, find and collect the right books on various theory, write down notes manually, do variations over the board instead of clicking through them real quick, etc.
Lol Kasparov speaks Russian and English doesn't he ?
Kasparov didn't learn English to read English Chess books. Fischer was singularly interested in Chess, not the Russian language, he just learned it to read their chess literature.
I think Kasparov read chess literature in English, and wrote some. Also, computers in the 1980s weren't as advanced as to affect the game of top playes much, however Kasparov showed an ability to adapt to computer preparation when it became important.
I can't say for sure which one is better, but I definitely PREFER Fischer, because of his complete and utter annihilation of many grandmasters.