Remind Me Never To Do That Again
Shoot off my mouth without checking the facts, that is. I took a quick look at the combined records of all AFC teams every year since 1970 (the year the AFL and NFL began playing regular season games together), and found that the AFC was 16 games over .500 in 1999, and an incredible 20 games over .500 in 1979. Since the merger, all told, the AFC is 60 games over .500 against the NFC in regular season games (and 4 games--all Super Bowls of course--under .500 in postseason games). I'd guess you could win a bar bet or two with that knowledge, since most people assume the AFC has been the weaker conference. Even during the AFC's long dry spell from 1984-1996, when they lost 13 consecutive Super Bowls, they were only 15 games under .500 in games with the NFC.
Dominating the other conference in the regular season does seem to have some predictive value to the Super Bowl. There have been 34 seasons since the merger; in six of those years (1973, 1983, 1984, 1990, 2000 and 2001) the AFC and NFC were exactly at .500, so there are 28 remaining seasons/Super Bowls to check. The team from the conference with the winning record went 17-11 in those games. However, you do not have to search hard for contrary evidence; the 2002 Tampa Bay Bucs, the 1999 St. Louis Rams and the 1996 Green Bay Packers all won the big game despite coming from the weaker conference in the regular season.