We like our 10-22 also but if its down to one rifle give me the AR 15. All round better for defense and hunting.
All my rifles are my "favorite".
Keeping only one? Not the AR, but the AK, hands down. For several reasons.
As regards hunting, I imagine in a real collapse the game that requires more than 22LR will be hunted to near extinction in a short time. We'll all be scrounging for squirrels, rabbits and the like.