I do think the balls make the biggest difference. How the ball spins, the trajectory, how it reacts from tight lies from the fairway, how it reacts from the rough, how it performs on/around the greens, and last but not least - how it reacts coming off the face of the putter....
I find it very telling that Watson chose to use the PROV1x immediately following his freedom to use another ball without contract.
Not suggesting it will be a great season for Watson, but I suspect it will be better than it has been while using the Volvik.
Often times, the confidence in equipment (including the ball) is the difference.
Not surprised he made the move to be honest. I think he's happy to be out from under the contractual obligations of using a ball he hasn't performed all that well with.