Hey there,
I'm not technical so I can't really go into why vbulletin is better than phpbb in terms of it's code...but i'm told it is
As far as a user standpoint (administrator) it offers alot of powerful features and everything is laid out in a very easy and straight forward way!
It's also very fast, vbulletin has a great support team and there are so many mods/hacks and skins available. Custom skins for vb are alot more popular than invision board of phpbb and that's one of the reasons I went with the product.
vbulletin has been around for along time, it's a commercial product and it's also very secure! phpbb had a huge bug last year that made alot of forums vunerable to basically being corrupted or something! I personally can't stand phpbb, it feels slow...the layout (default one) is very awkward, invision board has awful support and they charge for nearly everything!
vbulletins template system is also a big reason to choose this software, it's laid out in such a way that you can quickly and easily edit the code