Re: Browning X-Bolt or Winchester M70?
I have one of each, so very limited experience. For my daughters 12th birthday, I bought her an X Bolt micro in .243. I turned the trigger weight down a bit, mounted a leupold 2.5-8, and bought some 100 gr Federal at Walmart to get the brass. Off he bench, that combination was 3/4" (3shots/100 yds) all day, every day. Have not even bothered to build up a load for it.
I have a win 70 coyote light 270 wsm. First gun would not do better than 3-5" with Federal factory ammo; Winchester supreme would not stay on a 8 1/2x11" target. After looking it all over, I found a reamer mark (or gouge) 2/3 around inside of bore, 1/4" from muzzle. Sent it back to Winchester, and after 14 months and multiple phone calls, I received a replacement. New gun shoots good AFTER 9-12 rounds, will not shoot worth a hoot clean. After 20+ rounds, accuracy goes down hill. Roughest factory barrel I own.
One example of each really doesn't mean much, but those are my experiences.
I know have your search narrowed to Browning and Winchester, but I'd tell you to take a look at the Tikka T3.
Best of luck