Advisor moving to a different school, should I move with him?
There's no simple answer here. Contrary to "The Fire Guy," when I moved, all of my students stayed at their old institution—primarily for financial and personal reasons. However, I received approval from the department at my old university to continue advising the students who remained.

The big question that you haven't addressed is what you'd have left to do to finish at school A. Are you one or two years out from graduation, or more? And how much extra time would you need to spend at school B completing requirements? And are there other issues, such as teaching load and organizational duties, that may extend your time beyond what you'd have at school A?

As far as being involved in a lot of projects, that's a double-edged sword: you end up with an experience profile that's a mile wide, but not very deep. It's not something you tend to be able to convert into a PhD thesis relatively easily.