I'd try to manage to get a Winchester M-70 Fwt. Classic but of the two named, I'd probably opt for the Savage. I don't know that variant, but they have a classic style with walnut stock that looks good. I suspect the bluinng and overall QC is better than on the Remington.
I've seen some Rems that had the bolts turn a plum color and seen more with rust on the bolts than on any other brand, basing this on guns handled in stores. (New and used.)
Also, there is the issue of the M-700's trigger, the design dating back to the M-721-722 of the 1940's design frame. The DESIGNER (I think it was Mike Walker) warned Remington that he had made an error and offered to re-design the trigger to avoid accidental discharges. The company refused, because it'd reportedly add about a NICKEL to the cost of the rifle, and they wanted to market it at a certain price point. This sparked a nasty expose on NBC, and I basically agree that the problem needed exposure.
I realize that many here wil tell you that they have M-700's and like them. So be it. They do tend to be very accurate, and the cheapskate (in my opinion) extractor usually works. MOST owners don't have trigger issues.
But I'd sure think about a M-70, a CZ, or a Sako. Still, I know the Savage has some very enthusiastic followers on the Web. They seem to be regarded as a great value. Accuracy is said to be at least on par with Remington.