I could be mistaken... but aren't we talking about different frame sizes here?
IIRC, the 317 is a descendent of the Model 17, obviously a K-frame. The Model 63 is a J-frame, yes?
That right there is a point big enough to be considered. No J-frame has ever felt as right in my hand as, well, any K-frame, but that's just me.
Gotta say, Stan, the grips on that Model 63 you've pictured are gorgeous!
Attention Brass rats and other reloaders: I really need .327 Federal Magnum brass, no lot size too small. Tell me what caliber you need and I'll see what I have to swap. PM me and we'll discuss.