I’ve had lots of both...still have 3-308s.
They shoot the same ballet at the same velocity. Hard to imagine but they work about the same on game.
The advantages to a 308 are that it is a far more accurate cartridge and is easier to load for in my experience. I also believe it’s more popular abroad if that matters.
I’ve never understood people saying it doesn’t handle bullets above 165gr well either. 308s are just fine with 180 and 200gr projectiles. As in every bullet weight it’s about 75-100 FPS slower...no difference with heavier or lighter bullets. Frankly I see more variance barrel to barrel than I have between the two cases.
I prefer a 308 because my grandfather hunted with one...i don’t think for a second either is any different in the field. Having used both I know better.
