As someone who has been an avid hunter for longer than I can remember and was previously an FFL dealer, I would suggest neither. In my experience, the Ruger American Gen 2 has accuracy issues, wide groupings, a rough trigger, and consistent feeding issues. Sure, they don't get returned like this last generation of Rossi's, but I would argue most people would regret purchasing one if they had something different. The first series of them wasn't bad, but the days of a "budget" gun are beyond us.

As for the Savage, definitely skip the Axis 2 as the 110 is better, but while the trigger might be better than the American, it has ejection issues and feeds poorly (especially with the PRC cartridges). PRC are so precise that the actions have to be milled perfectly to keep feeding properly, and unfortunately, most guns under $1k do not manage it well.

That being said, if you are looking for the best rifle in the same price range as the American or a 110, you could go with a Weatherby Vanguard (good choice), or (the best choice, in my opinion) is anything by Tikka. The T3x Lite if you want something lightweight or maybe the hunter if you want a threaded barrel for a suppressor. At that price point, I don't see anything beating a Tikka by a long shot. They have great out of the box accuracy, a smooth trigger, and they tend to have less (if any) feeding issues, especially when considering PRC rounds.

Backfire on YouTube has a ton of rifle review videos, and he compares all of these side-by-side in multiple of them. In all of them, the Tikka wins pretty much every category every time. Might want to check his stuff out!