SS Dave;
I have given this some thought since you first posted it. I must admit (keep this quiet, please
that I am a real .22 fan. I have a safe full of them, both single shots and high end bolt action rifles. I go through one to two cases of GOOD .22 ammo per year.
I have both Stevens and Ballard actions. I chose a new Ballard barreled action (Badger barrel) for my "Frogmoor" and could not be happier in any way. My Ballard has double set triggers and Ron Long's "speed lock". It is a FINE combination.
Both Ballard and Stevens have the very desirable quality of having a "rocking block" which seats a match bullet in a tight match chamber. This is difficult in a straight falling block unless the top of the block is beveled like the original low-wall .22's.
The most important thing about a "shooting" .22 will be a match chamber. Any of the top rated barrel makers can supply a barrel that should satisfy the most discriminating. My Stevens 44 has a Shilen match barrel. My new Peregrine has a Shilen match barrel (hand lapped by Shilen).
I would suggest that ANY barrel for lead bullets be lapped by the manufacturer. Shilen charged me only $20.00 for that. I bought my Shilen Barrel direct from Shilen and it cost less than $200 delivered (a couple of years ago).
44 Stevens make up fine .22's. 44˝'s are even better. I would love to have a .22 made up on the "Ladies" 44˝ (044˝) action.
All of that said, if I had a choice and money didn't enter into it, I would choose the Ballard because of presently available parts (over the 44) and thru bolt stock. Keep in mind, that if you do not take special precautions, the Ballard's regularly split stocks at the wrist. This is solved by seriously glassing the inside of the stock at the wrist (info supplied by Ken Hurst before I had Bernie Harrell do my Frogmoor in this manner).
FWIW
Dale53