In the General Music Discussion thread of this forum, there is a "Bon Jovi Appreciation Thread" I started:http://forum.atu2.com/index.php/topic,2046.0.html
As the last reply there was made around a year ago, I don't really want to revive it and bump it up.
Maybe a decade ago, when Bon Jovi played in Ireland they did a cover of "One."
In the more recent years, they would do a snippet of Vertigo. Here is a clip I found on YouTube:http://www.youtube.com/watch?v=6ZCJiuZmR5c
While Bon Jovi has had great longevity and continued success in their careers, U2 have sold more records worldwide, played to more people, won more awards, and more importantly have kept the same lineup since the beginning.
In summary, I think there really is no "versus" in this fight. In fighting terms, you can't pit a light heavyweight like Bon Jovi against a heavyweight like U2. It would be better to just compare their similarities and shared musical values.