Of the two, I'd pick the ruger. Browning has two major problems with the abolt II.
one - they glue the barrels in now, so the action is a throwaway. Yea maybe some heat may break the epoxy loose, but the whole idea of a throwaway rifle sucks.
two - they mill the sides off a perfectly good action, making it weak around about 40% of the front ring. Stylish yes, strong and stable, no.
The ruger is a better choice. basic design, good extractor, real safety. The downside is the receivers are very hard, so you run a risk of cracking them when rebarreling, but this is a rare occurance. Bedding is a bit more difficult with the front screw pulling at an angle.
I still like the Winchester as a box stock rifle better than the remmie. It has a real safety and a less complex/more reliable trigger design, plus a real extractor, not a sliver of sheet metal. The remmie is the small block chevy of the rifle world, but if you plan to pretty much leave it alone the winnie is the hands down better choice.
Why not consider a savage? I'd take one over the abolt ii and ruger any day of the week. pillar bedded/free floated from the factory, pull button rifled barrel, real safety, accutrigger option, accuracy right out of the box that will blow away all rifles mentioned above (when looking at the entry level rifles, not the premium remmies in the HS Precsion stocks).
Hope not to fuel a remmie versus the world flame war here, but you remmie fans need to face the facts about stock rifle to stock rifle. The remmie is a few rungs down on the ladder. And yes I own/have owned multiples of all aforementioned rifles sans the abolt, but had a few of these in pieces in my hands to know them as well.