I have used both phpBB and vBulletin over the years for various sites. I used them for forum fan sites for games and for forums for various business's.
For the game sites we use to run, I preferred phpBB because you set it up for free and let the players who ran it customize it with very little experience. It is a good platform to learn on and easy to use.
For a more professional site or business, IMHO, vBulletin is the only way to go., it's fairly easy to integrate with your site and I never had any security issues like phpBB could have at times. For me though the look, feel and integration was always the big seller for us to purchase vBulletin.