PhpBB:
-very large user base and lots of developers , theme arists , etc.
-very large database of modifications , themes , developer resources , etc.
-Good with security , stability and usability(I have seem some really really massive forums too use it)
-Arguably Most popular of the three
-The newest version(3.06) has really improved a lot and it works beyond my expectations . Now runs with quick reply , and multiple captcha(including reCaptcha) systems , universal user reporting database system , etc. and lots more right out of the box . I currently use this and am highly satisfied .
-Modification installation is to be done manually using ftp and editing of files might be required for certain modifications(unless you are using their automod installer that is also available on their website)