I've not used phpbb in probably two decades, but not really comparable as one is paid and one is free. Or was... I assume it still is?

However, when I was hot and heavy in forums in the late 90s to early 2000s, vBulletin was my software of choice. It was uber stable (v3 was a workhorse) and have a massive community developing add-ons. After it was sold off (and subsequently ruined), the original developers left and created Xenforo. They've carried much of the same ethos that was around during the early vB days.