Shift is Partcle Pearl, Twisted is Pearl, both are asymetrical.
The Shift should start up sooner and handle more oil than the Twisted. Both will probably move more than what you have now, depending on the conditions you face. Really there are a ton of balls that will go above the Hot Rod, most everything you can find nowadays is going to be stronger.
If you want a step up from your Hot Rod and still be skid flip the T-Road Pearl is your ball. If you want more oil handling the T-Road Solid is a good choice. Most all of the current Storm balls use the same base cover, so the core strength is what separates them. If you want a strong core go with the Shift, if you prefer weaker cores the T-Road is what you want.
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-Clint