Very little Rob! It is lighter and quieter than the BJ and sound-wise the two are very alike (ie great!). The Session has a couple of extra sounds too - mine has the optional Blackface and Presence switches. The first is great for "glass" and the second flatters a Les Paul nicely.
Very chuffed with it and they are now sold as complete combos with a variety of options (cabinet finish, speaker). There a 45W version too.