The 317 is a pretty specialized piece. I have two, one 3" w/adj sights and one 1 7/8" w/fixed sights. The sights and light weight makes them both more difficult to shoot vs the M63. I also have a 4" M34 (Blue version of M63). Would choose the heavier steel frame gun if the only .22 I was going to own.
The M63 weighs twice as much as the 317s and the stainless frame is going to be more durable. Even at 24 oz, the M63 is still pretty much a light weight revolver, but much more durable/shootable than the 12.5 oz of the 317.
Lots of folks complain about the J Frame 22s double action trigger pull -- I've never found it objectionable and shoot the heck out of the two 317s and a 4" M34 double action.
My two biggest complaints with current S&Ws is front sight height and spurious sticky extraction issues with .22 revolvers. The M63 isn't a "gimme" when it comes to sticky free extraction -- no current S&W .22 revolver is.
FWIW,
Paul