You are getting GREAT answers. Only thing I perceive is you may not need, want or understand that.
You read like you never shoot far and only shoot deer. That's a nothing and either one would be fine for those needs. People talk about target. You don't do that. Non-issue.
Answers dealing with energy and bullet weight, surplus ammo (available for both), action length, bullet speed etc. are also probably not relevant. You might not have a need to understand the minor differences.
As soon as you mentioned "cheek weld", I had a red flag thrown up. To me that means you want to push your head into some kind of tight stock position that probably feels comfortable but also puts pressure on the gun that make it harder to repeat holds for accuracy.
I say use what you like. It will make no difference if your knowledge and needs are limited to 200 yard deer hunting. Enjoy both rifles.
You are correct in that I use my rifles primarily for deer hunting and I live in the Northeast. Unfortunately there are no ranges over 250yd.s near by me that I'm aware of.My gun club has a 250yd range that both guns shoot pretty accurately in. I just started playing around with loads again as I was just shooting150gr. Hornaday SSTs over Varget powder for both guns. I now have some 178gr.Amax coming and will try out the new ELD bullets. I also just broke down and bought a new Savage111 in 25-.06 and a Dillon press. As for the cheek weld comment, because most of my hunting shots don't afford a bench rest I like a stock that lines my eye up with the scope immediately when I bring the gun up.
My longest kill shot on a deer was approx. 350yd.s with my 1974 RugerM77 30-.06. I used to shoot woodchucks out to about 600yd.s with my old Remington25-.06 off my dad's porch down in PA. Where I live now you don't even see chucks anymore probably due to coyotes. I'm building my own 500yd. range on some land I just bought and I plan on doing some predator hunting there.