I like invision better... intergration... ummm... Jesus*?

[* in bible school TJ learn I Corinth teached Jesus is the solution to every problem. Not sure of the answer he is sure Jesus will work... ]

phpbb vs ipb

IPB has more features, but it's not free or open source.

For open source, free, and super easy integration I'd personally recomend Simple Machines.

It depends what CMS.
phpbb is already integrated for some of them.

Invision board is much better, but the latest versions have only a short trial period before you need to pay.

I'm closing this topic since it's discussed in perhaps 10 other threads on this forum. just check the search link posted.

PHPBB simpler to use and easier to integrate with your website. 1000s of themes available and now PHPBB3 (under development) you have many features which you get mostly in paid BB softwares.
so PHPBB is the best.
Demo : free forum