OKay I'll be the one to answer your question in a nutshell...
Ruger 10/22
+Has a better action
+Jams less
+A lot more accessories can be added
Remington 597
+Is more accurate
+Cheaper
Overall: All of the differences above are just slightly more or less than the other with the exception of the accessories although u can get the 597 in VTR which is pretty bad4ss. I shot my friends 10/22's tons of times and i own the Remington 597 myself. Honestly when people say you can't go wrong with either, you really can't here. You narrowed it down to the top two .22's rifles that exist and both are tied for first so voila!
...but because "I" have a 597 i like mine more hehe It's even in my avatar