I recommend you to try bbPress. It’s easy to install, there are lots of additional plugins, the loading time is better than with phpBB. Also, you don’t have to create any bridges for you forum integration with site.
phpBB is much more complex, it’s complicated to create and install mods. Also, it’s not so seo friendly as bbpress is and you will have to create the integration bridge between your phpbb forum and site.
I have tried phpbb and it was like a nightmare, but then I moved my forum items to bbPress (with cms2cms converter), so now I’m pretty satisfied with this.
So, I recommend you bbPress definitely!