Charles Sullivan (link) gives us the best evidence-based answer to this much debated question.
The clear winner is - Bobby Fischer.
The project undertaken by Charles Sullivan applied some of the ideas outlined in "Computer Analysis of World Chess Champions" by Matej Guid and Ivan Bratko (1) (pdf link) and also applied ideas from Jeff Sonas at the ChessMetrics site.
The entire playing careers of the world's greatest players (from Morphy to Anand) were computer analyzed - giving a total of 617,446 positions from 18,785 games.
Ranking of Champions Based on Best Time Period:1 year ....... Bobby Fischer
2 years ..... Bobby Fischer
3 years ..... Bobby Fischer
5 years ..... Bobby Fischer
10 years ... Bobby Fischer
15 years ... Capablanca (2nd Smyslov; =3rd Karpov / Fischer / Botvinnik / Kasparov / Kramnik)
Fischer does not top the 15 year table (his best 15-year period includes the teenage years before he became an elite Grandmaster).
Computer analysis of World Chess Champions
Matej Guid and Ivan Bratko
University of Ljubljana,
Faculty of Computer and Information Science,
Artificial Intelligence Laboratory,
Tags - Botvinnik - Bobby Fischer - Capablanca - Charles Sullivan - Chess Player - ChessMetrics - Grandmaster - Greatest - Karpov - Kasparov - Kramnik - Smyslov - World Chess Champion -