I personally would pick Xenforo. It seems like vBulletin has been really going downhill as of late, and support for Xenforo just keeps getting stronger.
Vbulletin is a better software to use well VB4/VB3 were, however with the path its taking at the moment, i won't be surprised if they shut it down in a few years due to how many people are selling licenses and moving to Xenforo.
Xenforo if i was you, it has some pretty great support staff aswell.
As a user, I think I like vB better than XF. Perhaps because I've been using vB longer. XF looks nice, but there are some parts of its appearance and features which I don't like. I'm more comfortable with vB. Unfortunately I never run it as a moderator or an administrator so I can't say how much trouble each software brings to the management.
If it was between XenForo and vBulletin then, I'd probably pick Xenforo as they just seem to be rushing the new versions of vBulletin, these days.
It just seems like the management is just trying to make some quick money by pushing out releases as fast as possible.