597.
I have one of each. I prefer the 597. Here's why:
It is a great little firearm "out of the box". Short of getting some extra 10-rd. magazines and the Remington scope mount (and a scope, of course), the only thing you'll need to do is put on some swivel studs and a sling. I used Uncle Mike's studs and nylon sling. I drilled the stock myself (look for the most solid section at the front of the stock) and put the stuff on.
It is accurate, feels good, reliable (be sure to load the magazines correctly and you won't have a problem), and the controls are where my other Remingtons have them...
My 10/22 is also a good rifle. It, too, is accurate and reliable. However, if you want more than 10-rd. magazines, you'll pay dearly for them now. And, you'll fall into the trap of "how many variations of the rifle can I make?" One won't be enough. You'll have so many parts you'll need 3 of 'em just to make it worth having all the extra parts! There are some functional differences between the two.
The Remington can be disassembled and fired that way (ssssshhhhhhhh.....)or so I've read; because of its design. It also has a bolt-hold-open feature when the magazine is empty, which the Ruger needs an extra part for. Etc., etc., etc.'
So, right out of the box, the Remington is better, in my experience. I like my 597 a LOT!