Kasparov or Karpov

Both great players but Kasparov stronger player because younger and more active/dynamic player using modern tools. You cant split them though, they were the best player of their time. Karpov much more solid player with most tournament wins of all time in chess history. 

Karpov. 

Kasparov great attacker but I see Karpov as much more completed player, and person as well. 

Apart from issue with RJF in 1975 which was not his fault I never heard bad word about Karpov, and in his appearances he was always acting like Gentleman which can not be told for GK.

Karpov respected system (FIDE) altough he was perhaps aware of dificiencies, GK made paralel system which lasted few years only or as long he had interest in it. 

Karpov held crown 10 years, plus few years with Fide in 90s. Kasparov was champion for 10 years too, some years with paralel (private) organisation, match against Anand was 1995 think. Remaining 5 years on top can not be counted since he outplayed Shirov in 1998 not giving him match which he deserved and so on..... when Karpov did something similar?

Later on he, GK, tried to do rematch against Kramnik based on what? Why he did not go through full candidates cycle?  Karpov did it in the year when GK faced Short.

GK wasted to much energy on things outside chess which he did not actually need, this is why I asume Karpov as much optimized and stable as person. 

I definitely like Karpov more, but Kasparov brought masterpieces to the chess board and is considered by many to be the greatest to ever touch the chess pieces in history. He modernized opening prep and is an influence to millions around the world. He had an aggressive and tactical playstyle, who was able to calculate complicated positions with efficiency and accuracy. Karpov was the constrictor who would grind you to dust slowly, marking with his highly accurate play, being able to crush somebody with the slightest of inaccuracies in complicated positions, with his broad knowledge of positional play. They played many many games, majority of them which ended up in a draw, but in the end both world champions were phenomenal players of their time and held the crown for over a decade each.

There's an old book called How Karpov Wins that pretty much gives away his big secret: develop everything to decent squares, slowly improve your position and look for a tactical shot as well and then, even if no brilliancies show up, grind the crap out of your poor opponent.

Karpov. 

Kasparov has beaten Karpov 28 to 21, with 121 draws.

kasparov

Both are phenomenal, Kasparov overall is the more accomplished player, but Karpov is easily one of the greatest of all time. Both pushed each other to their extremes, without Karpov, there would be no Kasparov.

Gazza.

Kasparov was better, since he was higher rated and never lost a match to Karpov after becoming World Champion. However, Karpov was also phenomenal. I consider Kasparov the second greatest player of all time, after Fischer, and Karpov 4th, with Carlsen in between.

Karpov is much more humble and pleasant as a person. He even still plays chess semi-competitively and has continued to be a very strong player even after many years (in fact he recently defeated Karjakin in a classical game).

Kasparov may have had a higher peak rating, longer period as world #1, and achieved status as a cultural icon, but Karpov is a titan in his own right (and he didn't have to resort to having extreme ideologies to do it).

Karpov.

tiger or anaconda?  prefer cats to snakes.

Kasparov

After recent events I guess it goes without saying that as a human being, Kasparov is years ahead.

On the board is maybe still debatable but results strongly suggests Kasparov is better there as well... I like Kasparov's attacking chess, but he's sort of a d*ck on the board. And I also like Karpov's prophylaxis style, and I haven't seen many incidents of him not being a gentleman on the board and actually heard some nice stories about him, but I guess that gets overshadowed when you support mass murderers dictators. He could learn a thing or two from from Grischuk and Spassky

Kasparov games are Show Time. Karpov's game are Cold Logic.

Too generic an aphorism. Here is a game where Karpov made an intuitive, half-wrong, half-correct bishop sacrifice, and won the game in great style, being a whole rook down.