I have them both. The Breeze goes longer and snap harder in the backend. The SN is milder by comparison but it better be darned dry and you better not have any carrydown whatsoever. On some light oil conditions, you could go from the Breeze and drop down to the SuperNatural int he 3rd game. The SN is definitely a step down from the Breeze.
The SN has the stronger core, but the Breeze's coverstock is more adjustable. I've taken by Breeze from 2000 to 3000 to 4000 dull and polished and used it at all stages. My most useful stage was 3000 grit dull. Smoother and more controllable and less susceptible than when polished, but still plenty easy to get thru the heads on light oil.
Which you need depends more on what is not working now, what amount of oil you start with in league, your hand (revs, ball speed, etc.) and how dry it gets during the transition and the 3rd game. Also you can play deeper with the Breeze, where the SN is still an outside-the-3rd-arrow type of ball. It has more recovery than most urethanes but never what a resin ball can give you.