I don't own both, so I probably shouldn't respond.....
But I've owned a 10/22 Deluxe since 1981. It has been utterly reliable and shockingly accurate. It might not be "match grade" but it shoots CCI Mini Mags under 3/4" at 50 regularly and is plenty accurate enough to bean a squirrel on the noggin as far off as I care to shoot at one. I have shot who knows how many thousands of rounds through it and am on my third barrel. It is scoped with a 4-12 A.0. Bushnell Banner.
As much as I like MY 10/22, the current production leaves me cold. If I were buying today, I'd opt for the Remington 597. It simply seems to me to be the better value, being more carefully made out of better stuff and at a cheaper price. What I would rather have, however, is the T/C semi-auto, but I have yet to see more than one of them in the flesh and I didn't have any jack in my jeans when I did, or it would have come home with me.
While I have not owned a 597, and know that they had feeding issues early on, a pal of mine has a late production 597 that is simply a stellar little semi-auto .22 and edges out my 10/22 in the accuracy department, though not enough to make a squirrel notice. I really like the fit of the stock, which is an admittedly subjective thing. It feels and looks "all grown up," unlike the new 10/22's, which look and feel more like toys, to me.
YMMV, and all of that......
-JP