I imagine it's like performing a task in software ("big" brain, cerebrum) or hardware (cerebellum). One of them is faster and more efficient but very specialize

I imagine it's like performing a task in software ("big" brain, cerebrum) or hardware (cerebellum). One of them is faster and more efficient but very specialized. If it breaks you're left with the task being performed slower and less efficiently on the brain that can execute arbitrary code. But I can't imagine any change in this split in responsibilities will happen on human relevant timescales. The cerebellum is probably not evolving very fast anyway, while the cerebrum might evolve comparatively faster but it has no pressure to do it. And "faster" still means tens of thousands of years.