Would the Grandmasters of today defeat the old timers of a hundred years ago? Back in 2006 there was a Chessbase article showing the percentage of moves played by the top 14 players of all time (up until that time) and how they matched up against engine moves. Capablanca emerged the winner ahead of Petrosian, Karpov and Kramnik.
Unfortunately Elo ratings can't be used to make comparisons because a 2400 rating of yesteryear does not translate into a 2400 rating of today. The average Elo rating of top players has risen; I remember when a “strong” GM was 2500 and 2600's were referred to as “Super-GM's.” It has something to do with rating inflation...see below.
Arpad Elo argued that is was impossible to use ratings to compare players from different eras because ratings measure a player's performance against his contemporaries. Claude Bloodgood is a good example. He became one of the highest rated players in the U.S. by playing “tournaments” in prison where he routinely defeated very poor players, even rank beginners. If you only gain one point per game, win enough games and you'll eventually be rated very high.
Jeff Sonas of Chessmetrics also says it is impossible to compare the strength of players from different eras because, like Elo said, a rating only indicates the level of dominance of a player against contemporary peers; it says nothing about whether the player is stronger or weaker in actual technical skill than a player far removed from them in time. That means you can't compare Fischer to Capablanca as to who was the better player.
Back in 2007 a project was conducted using Rybka 2.3.2 and the players with the best 15-year averages were Capablanca, Karpov and Kramnik, Smyslov and Kasparov, Fischer, Botvinnik and Spassky and Petrosian, Anand, Tahl, Alekhine and Lasker, Euwe followed by Steinitz.
What do the GM's themselves think? In 1964 Bobby Fischer listed his top 10 in Chessworld magazine as: Morphy, Staunton, Steinitz, Tarrasch, Chigorin, Alekhine, Capablanca, Spassky, Tahl, Reshevsky. He considered Morphy the best, saying "In a set match he would beat anyone alive today." In 1970 Fischer altered his list a bit, listing Morphy, Steinitz, Capablanca, Botvinnik, Petrosian, Tahl, Spassky, Reshevsky, Svetozar Gligorić and Bent Larsen as the greatest players in history.
In a 1992 GM Miguel Quinteros thought Fischer was the greatest of all time. In 2000 Anand's list was Fischer, Morphy, Lasker, Capablanca, Steinitz, Tahl, Korchnoi, Keres, Karpov and Kasparov.
In 2001 a poll of Chess Informant readers for the ten greatest of the 20th century were Fischer, Kasparov, Alekhine, Capablanca, Botvinnik, Karpov, Tahl, Lasker, Anand and Korchnoi.
In a 2012 interview, Levon Aronian stated that he considered Alekhine the greatest player of all time and Magnus Carlsen said that Kasparov is the greatest player of all time, adding that while Fischer may have been better at his best, Kasparov remained at the top for much longer.
The question is, can some kind of rating adjustment be made so that players of different eras can be compared? Mark Glickman of the United States Chess Federation’s ratings committee said, “It is possible to say how much better Capablanca was than his contemporaries,” adding “If it were possible to put Capablanca in a time machine and transport him to this time, it would be virtually impossible to predict how strong he would be.” Glickman pointed out that because today's players have access to computers and databases they know more than their predecessors and so are better, but what would happen if Capablanca were transported to modern times and allowed time to “catch up.” There's no way of knowing how he'd react.
In the United States, instead of rating inflation, ratings are deflating. Blame the kids for it!! Young players (who make up more than half of the USCF membership) drag average ratings down because they improve faster than the rating system can keep up.
On the other hand FIDE ratings are inflating. According to Glickman it's because it used to be that players needed to have a rating of at least 2200 to be rated, but not any more. In fact, it used to be that Swiss System tournaments were not rated, only international round robins. The result is that higher-rated players feast on the lower-rated ones just like Bloodgood was doing in prison.
According to Glickman Garry Kasparov was pretty close when he wrote that the rating difference between the No. 1 player and the No. 2 player was a good determinant of who was the most dominant player ever. By that measure, since ratings began, Bobby Fischer was No. 1, and Kasparov himself was No. 2. But again, this only tells us how much better than their peers a player was, not how they compare across time.
However, in a 2002 paper Glickman used statistical analysis to rank the best players of all time and came up with the following ranks: 1-Lasker, 2-Capablanca, 3-Fischer, 4-Alekhine and 5-Kasparov.
So, you just can't say who was better, but for me, the games played by the old timers are a whole lot more interesting.