As a general rule of thumb, always match the breaker to the panel. Do not intermix brands, even though the typical 1" stab-in breaker will fit in any 1" panel.
All of the breaker panels have manufacturer's instructions that say you can only use that brand of breakers in that panel. In general it is UL's position that all manufacturer's instructions are 110.3(B) instructions and must be complied with, except in this case where UL can make more money by "classifying" other breakers to be used in violation of the manufacturer's instructions.
GE's can be tricky. Apparently they're just SLIGHTLY different than a CH or Murray; we used CH breakers in an old GE panel on a remodel. Had maybe 5 callbacks about the oven not working. Apparently the strain of the 8AWG wire bend inside the panel was enough to bring the breakers off of the bus.