My guess is the treble response would increase, and maybe the bass response would reduce - much like 'neck' and 'bridge' pickups on a 'solid' or 'semi'... I've never tried it, so I could be completely wrong!!

Fishman do make a 'left handed' version, so maybe there are differences in characteristics across the pickup itself...

I suppose the size and position of the soundhole in relation to the bridge could make a difference from one make of guitar to another, too.