I've owned several of the SS/Synthetic Hawkeyes. Most will shoot right at 1" or maybe a bit better. If you want a cheaper gun to throw on a 4-wheeler or for tough duty one of the Ruger All Weather rifles is hard to beat.
If you want a quality wood/blue gun the Ruger ain't bad. But for very little more money the Winchester is definately a step up. I think you'll probably get perfectly acceptable accuracy with a Ruger, but you are more likely to get bragging size groups with the Winchester.