The FBI's duty buck was and perhaps still is #4 buck. I have noted wider dispersion with Winchester #4 than most 00, but my testing was by no means extensive.
I've a sneaky suspicion that 1 buck may possibly be the closest to an all around buck size, but haven't done much shooting with same.
For sporting use, such as deer hunting, I'd want to stick to 00 or 000. Longer ranges mean bigger pellets for retained energy. All else equal, tighter patterns also.