45+ years of experience leads to my thoughts on this:
1. Deer: 270 Win or 270 Weatherby Magnum. Hunting area parameters make the decision. Close (300 yards) in, 270, long range wide open, the WeeBee.
2. Black Bear: Same as deer. Usually 270 as most shots are reasonably close.
3. Sheep: Although I have killed them with both the 270 Win and 300 Weatherby, my nod goes to the uber flat shooting 270 Weatherby Magnum. Light, and Deadly to extreme range.
4. Moose: 300 Weatherby Magnum. Face Plant every single time. Taken them with everything from a 25-06 to a 375. The 300 WeeBee gets my nod as best overall performer.
5. Elk: Either the 270 or 300 Weatherby Magnums. Both provide excellent long range performance yet sacrifice nothing for closer range shots.
All of that said, I will use the same crossbow (Excalibur Matrix 380) for any and all on this list
Cheers,
Nog