Free: Contests & Raffles.
Neither of those. The Tikka is light, and the 7 Mag has a good amount of recoil. Too much for a lightweight rifle such as the Tikka, in my opinion. And the Remington 700, I've been hearing of too many issues lately. I'd go with a Savage 110, Ruger 77, or possibly a Weatherby Vanguard.
Put a Sims pad on a Tikka and you'll wonder what all the fuss is about. My wife even enjoys shooting it and she hates dang near every 308 I own. Want to reduce recoil even more? Load it up with Barnes 120TTSX and you'll think you are shooting a 7-08.
If you’re looking strictly for “out of box” accuracy, I would favor the Tikka T3 between the two you have asked about. An interesting test would be to take ten out-of-box T3s, ten out-of-box 700s and run an accuracy test between them. I believe the Tikkas would have a slight edge. I’ve not known of a Tikka T3 that didn’t shoot well out of the box.That said, no custom rifle makers that I’m aware of uses Tikka actions. Many, if not a majority use 700 actions. With work, a 700 can usually become as or more accurate than any other actioned rifle.As far as aesthetics go, the Tikkas generally don’t score well - some believe they look and feel cheap. If that bothers you, get a 700 or expand your search to some of the other makes mentioned.