Bret was my hero as a kid and I was saddened by the way his WWF career ended. In later years his bitterness has been overbearing but nothing can diminish his catalog of great matches, he was a much better face than Triple H and also a pretty good heel.
From 1999-2001 I was a huge Triple H fan, he was my favourite of that era without a doubt, and up until 2006 I still mostly enjoyed his work, however I've always found him a smug, obnoxious prick as a face and have rarely enjoyed anything he has been involved in since he turned face in spring 2006.
Triple H is the better mic worker but Bret did enough to get his point over.
In the ring Bret has the superior body of work IMO, he could have a great match with anyone and was just as good a brawler as HHH, he just didn't get involved in many matches that used weapons, his brawls with Diesel and Bulldog in 95 were great. However when he did have one that used weapons at WrestleMania 13 he delivered a match that stands head and shoulders over any match Triple H has had.
in 2000 Triple H had as good a single year as anyone has ever had as far as consistency goes and while most of his classics are gimmick matches he has had some very good regular matches as well.
The truth is that what Bret said about Triple H was so overblown it negated any points he may have had, and the sad thing is him and Triple H would have made for great opponents in my view.
In the end for me it comes down to the fact Bret is retired and I've been sick of the sight of Triple H for half a decade, so the question is which guys matches would I dig out just to sit and enjoy a good wrestling match as I don't collect promos, and while Triple H has 2 or 3 I'd watch again, Bret has dozens I find infinitely watchable, so he gets my vote.