Generally speaking, bolt guns are usually more accurate. They can afford to have tighter tolerances as the action is processed more slowly.
In this particular case, the stock Win Wildcat (which is the TOZ 78 from the Tula plant in Russia) will likely be the more accurate than the stock 10/22 (by a long shot). I don't have one yet to confirm (have a Varmint/Target on order but they are not out just yet) but the results people have gotten from the Sporter version seems to show this to be the case. Of the few 10/22s I've shot in stock form (most of them mine), they've all had a very hard time consistantly shooting less than 1" at 50 yds, even with higher grade ammo. 1.5" is common though. The Wildcat should be able to go under this easily.
The 10/22, however, can be built up into a real tackdriver with aftermarket parts. This is the Ruger's biggest plus, the ease of being able to work it over.