I have little doubt you will be very pleased with your new 63. I've owned 5 or 6 through the years, and they were all very nice revolvers; a great balance of compactness, carry-ability, and precision.
Regarding accuracy and weight compared to the various 617s and K-frame rimfires, first, I believe there is little difference in the
mechanical precision between the K and J frame .22 revolvers, meaning, if you put them in a Ransom rest, they would be very close in accuracy, while showing the usual individual preferences for specific brands and lots of ammunition. I would say the same about a skilled shooter firing them from a rest in single-action mode. Any difference would be the normal variability from revolver to revolver.
The lighter and smoother double-action of the K-frames, along with their greater mass, however, make them easier to shoot in that mode, in my experience. Getting grips for the J-frame that match your hands, and much practice, will go a long way in narrowing that gap, though. In the field, from normal shooting positions, the heavier revolver will be easier to shoot accurately, if you're okay lugging one around...and there is the rub. The K-frames, especially those with the full lugs and longer barrels, are less carry-able and are quite the chunk, so one's priorities will dictate which better suits your needs.
From a pure precision perspective, firing in double action will never produce the same accuracy as steady, single-action firing, and, in this regard, the incomparable single-action Freedom Arms 83, or the smaller 97, will likely be more accurate than most any S&W, unless one has it customized.
For me, I went with a vintage 63 and installed a Hart barrel that I machined for scope use. Even with the heavy barrel and the scope and rings, at 35 oz, it still weighs considerably less than most 617s, even the 4"ers, but I would put it up against even a Freedom Arms revolver when shooting it in single action mode from a bench rest. I get 1/2" to 3/4" groups at 25 yards, but hold and follow through are very critical; I really have to concentrate and be very consistent in my technique to realize that level of accuracy.
Early testing before I lightened the barrel a bit:
I also recently bought a 317 for carrying in my cycling jersey pocket. It is incredibly light, and everyone invariably does a double take when hefting it, but it represents the other side of the spectrum on shoot-ability, especially in DA. Still, as Gerald mentioned, practice and discipline will yield surprising accuracy. I did have a hard time paying the same price for this all aluminum wonder that S&W gets for its current stainless 63s. In the end, though, I would say it's worth it for my needs.