Technically, InvisionBoard executes fewer queries which makes its performance slightly better than phpBB, not to mention that phpBB comes with quite a few bugs and some security issues (at least the last time I checked). On the other hand, phpBB has been around for quite some time longer than Invision, so naturally, this leads to more community experience with the board if anything goes wrong, and possibly some more hacks and additions.

"Stephen Wolfram is the creator of Mathematica and is widely regarded as the most important innovator in scientific and technical computing today." - Stephen Wolfram