It hurt to do it but I voted for the Winchester. Both are good guns but the newer construction - baseline-- Remington s are kinda junky IMO as far as fit and finish. I still own a lot of Remington rifles and my deer gun is a 660 Mohawk in 308. But the Big Green just isn't what it once was. I am seeing a lot of rusting issues from stuff made in the last 15 years. Winchester is not what they were 50 years ago either, but the over all Model 70 design is very sound and has stood in good stead for 100 years. I have not picked up the new Featherweights but I own a pre-64 Featherweight and like that gun more than I do most of my kin![:D] Both the guns you mention are good guns and will stand good for you for life and you can drop any deer in the woods with a 308 (can't go wrong there). I'm just a rifle snob and love older rifles. I plan on buying at least two new rifles b4 i punch out --- both will be 308 winchester one will be a TC Icon the other will be a Sako Finlight 75. These represent (IMO) the difference between a good rifle and a great rifle in the full production lines available today.
It matters not the weapon nor its caliber, rather the caliber of the one who wields it.