The triggers suck on both. The Remington triggers made since 2007 are safe, but not very good. The Remington triggers made 1946-2006 were a flawed design that in rare cases could release the firing pin with no trigger pull. While improperly adjusted triggers can cause the same issues, the Walker designed trigger could do it regardless of trigger settings.
The Accutrigger is designed so that it is possible to pull the trigger without depressing the blade in the center. When this happens the sear is released, but the firing pin block prevents the gun from firing. You get a loud click, but no boom. The only fix is to cycle the action to re-cock the rifle and get a proper grip on the trigger when you try again. It doesn't happen often, but it does happen, especially when wearing gloves.
Personally I'd buy the Ruger American and have a better rifle than either for less money. Of your choices It'd be close, but I'd probably go Savage in a 308, but in a long action would go Remington. Savage long actions are loooong and ungainly.