I shoot both and I guess it kinda depends how you hunt squirrels. If you do a lot of walking, might want to keep things as light as possible. With the Ruger 10/22, the heavy barrels are a lot more accurate, but I wouldn't want to lug one of mine around all day.
Compared to a plain jane 10/22 Ruger carbine, the Rem. Mod #5 with a 22" bbl will be just a tad heavier too. If you need a follow-up shot, the Ruger is a lot quicker than the bolt gun.
If you hunt by setting in one spot and snipe e'm out to 60 or 70 yards, the weight won't really matter, but that fast 2nd shot is great if you need it! Many times I'll shoot the first one only to have a second one pop-up to see whats going on!
This is just my opinion, for my type of squrrel hunting, so take it for what its worth. I could grab anything in the pictures. I always go with the 10/22 Deluxe carbine, it has a 3x9 40mm scope, (3rd one down). It's plenty for what I do and has killed them by the bushel basket. Light and accurate.
Good luck which ever way you go, you can't go wrong with either choice! Ken