The last year the NFC had a winning record against the AFC in the regular season was 1995. Since then, the AFC has won 444 of 806 regular season games between the two, or 55.1%, with a high water mark of winning 44 of 64 interconference games in 2004.
Over the 1983-1996 seasons, when "everybody" knew the NFC was so much better than the AFC because the NFC won the Super Bowl every year, the NFC had a winning regular season record against the AFC in 5 of those fourteen seasons. Overall, the NFC had a cumulative regular season record of 377-360-1 against the AFC during that run of Super Bowl dominance. Their high-water mark was 1991, when they went 33-19 against the AFC. Outside that year, though, the NFC was a mere 3 games better than the AFC in the regular season over the remaining thirteen years.
Overall, since the merger, the AFC has a record of 1058-951-11 against the NFC, or a .527 clip, and has a yearly record of 23-8-8 against the NFC. To put it even more starkly, the NFC has been clearly better than the AFC for two separate stretches: 1970-71, when the AFC was still reaching parity, and 1989-95, when the NFC went 5-1-1 against the AFC. In the other 30 years, though, the AFC is 22-1-7 in interconference games. The facts are pretty simple: since 1972, if you've been watching the NFC more than the AFC, you've been watching inferior football. You have my sympathies for your past mistakes, but are welcome to repent at any time.
Thanks to the 2008 NFL Record & Fact Book for interconference records for 1970-2007 (p.584). 2008 interconference records were calculated by yours truly from 2008 standings.
UPDATE (7/8/09 0009 CT): Fixed a typo-replaced the wrong number.
UPDATE (7/10/09 1947 CT): Actually bothered to edit post.
UPDATE (12/20/09 1941 CT): Fixed some math errors I'd been meaning to for months.