I've always thought of phpbb as the best (popular) forum software out there.
Invision I can't really say much about... but it just seems generally annoying, with the amount of times you have to click to get somewhere, mostly.
But phpbb is great. In fact, I used it to base my own website off of - even though the only part of what's left is the templating system, which actually sucks quite a lot but I couldn't be bothered to code my own
I should get round to that sometime.
What really annoys me is people are always moving away from phpbb. Linuxforums and Overclocked Remix both used to use phpbb. And now they use freakin vBulletin. -_-
I want to help make people realize that phpbb really is the best there is. But nobody listens to me!