They are both decent .22's in my experience with both of them. That being said, others have complained about the 10/22 being less than accurate, which I never really noticed; and the 597 being very picky about ammo, which I also never had a problem with. So you should be happy with whichever one you do decide to go with...
But, for what it's worth, I sold them both and bought a TC R-55. The R-55 blows them both out of the water! It is the ultimate semi-auto .22, IMO.