It doesn't matter "which" board you use.
PhpBB, I believe, is more for "experimental" and "fun" use.
It gives you the ability to do limited features, experimenting the "ways" of a messageboard/forum.
Invision Board is more on the "professional" seriously personal or business forum.
Either way, Invision Board is a security heavy forum, mostly why people prefer this one.
It gives you more than 72 options, enough to leave you on the forum for a few days
.
VBulletin Board is more like Invision Board, just, many companies use it because of their low price rather than high price.
It is below average on terms competing with Invision Board, but, at the same time, it has quite some unique features.
It is really up to "you" to evaluate and decide which forum is best for you.
My advice is to test all three forums or every forum you find.