I shoot a few Savage rifles and I do have one Ruger American, accuracy has been great out of them. I don't see any issues with accuracy with either one, plenty good enough to take deer. You just have to decide which rifle has the qualities youre looking for in your deer rifle.
The first issue with both rifles is the stock usually, but both models of Savage rifles you looked at should have the Accustock. The Accustock is a much better stock than the Ruger American offers currently. There are Boyd's stocks for the Ruger's that will give you a much more rigid stock, but they add weight.
Which bri gs the second iissue you need to decide if it matters to you or not is the weight of the rifles. IMO this is the biggest issue with the rifles you're looking at. Depending on what you choose for scope and scope mounts, you can easily keep the Ruger under 8 lbs and the Savage you looked at will probably end up just north of 10 lbs. I know the style of hunting I normally do there is no way I'd use a 10 lbs rifle.
In this case even with the flexible stock of the Ruger, it's what I'd choose because you said it would be a deer rifle. I'll always choose the lighter rifle when it comes to hunting as long as it is accurate enough. While its stock is flexible, I'm more than capable of shooting a MOA group at 300 yards with my rifle from off a bipod in the prone position.