My first handgun was a 3 screw single six. Can't speak highly enough about it. Never should have sold it. That said, I enjoy my bearcat for occasions you said, hiking, fishing, whenever you are not in the woods seriously hunting, just want something in your back pocket. That is this guns best feature, its compact size, as well as reliability.
From a bench rest, both guns are about the same, accuracy wise. A lot of people though, have a hard time shooting smaller frame guns accurately. The small sights and grips, and light weight coupled with today's heavy trigger pulls make off hand shooting difficult, and less precise then with a full size gun.
If you are looking for a serious hunting rimfire, then the single six, or a scope sighted Ruger auto pistol, for that matter, would be my first choice. If you plan on using a holster, then I would go for the single six, as I don't think you will notice the weight difference between it and the bearcat. If you are looking for maximum weight savings, and plan to carry in your jeans or jacket pocket, the the bearcat will serve you well.
Larry