I think you can’t compare both forums, bbpress is still in an early stadium.
bbpress is very cool because it’s very easy to combine bbpress with wordpress (and buddypress)
EDIT: and bbpress is more spamproof (at least for me)
I think bbpress is relatively faster when compared to phpbb.
According to _ck_ bbPress is faster. According to Sam phpBB is “probably” faster in some situations, in others bbPress is faster. In most situations I’d assume bbPress would load paages faster simply because it generally has a lot less to do, both content wise (less features = less HTML/CSS) and processing wise. The only way to tell would be to bench test two identical setups, but I haven’t heard of anyone doing that before.
In most practical situations I doubt the performance issues are a real issue though. The way you code your theme will probably have more effect on page load times than anything in the backend.
This is all just guess work though.
What about queries, php etc.