Phoneman: I have a bunch of Model 63's, 34's and 651's both 4" and 2" types - and indeed they are "tasking" to shoot "accurately" - in my opinion.
I can shoot heavier 4" barreled rimfire and centerfire pistols more accurately.
Its been a long time since I shot a Bearcat but I am sure I would should my 63's better.
Never shot an adjustable sight Bearcat.
I would think the Model 63 would hold the relative accuracy edge over the Bearcats for most larger framed shooters like me.
If you are trying for or need more accuracy i say get a "K" framed Smith.
Having said these things my main Model 63 (4") is a constant companion of mine when I am afield. I just am aware of its accuracy and make do.
By the way what price range would your Model 63 be in if you decide to sell it?
Best of luck to you with whichever you sell.
Hold into the wind
VarmintGuy