The most important parameter to consider up front, is integration.
- phpBB is a CMS on its own.
- Any Drupal based forum solution uses Drupal as CMS.
"CMS" means that it will use its own database, its own log-in system, its own management, and its own moderation environment.
It also means that you are mixing technologies, such as Database abstraction, scaling and deployment. But for you, probably more important: instead of learning one layout/design layer (themeing) you have to learn two. Instead of maintaining security releases for one system, you manage two. Instead of finding one expert to build and maintain your site, you must find one that knows both, or find two.
Small features such as "log me in with the same role (admin) on the forum when I am logged in on the Drupal-environment" are hard.
Small features such as "include search results from the forum in main site search" are near impossible.
I advise people to choose external forum software, only if they don't mind the following:
Obviously it is not required to have separate domains for phpBB and Drupal, but in practice that is what you are building: two separate sites. Which may have some interlinked features, but integration is minimal.
Do you mind building two separate sites? Then choose an integrated solution.
Do you not mind having to separated environments? Then go for phpBB.