I've had a few Remington 700s. I've worked on a couple more.
The extractors SUCK. I replaced TWO in one gun. There was obviously something wrong with it. Finally went with a Sako style. Round count was under 100 and all factory 7mm mag.
The safety only blocks the trigger/sear and not the striker.
The barrel quality is spotty. You may get a good one, you may not.
I would take a new Winchester 70 classic any day of the week over the Remington. They cost a bit more, though. I've got one in .338 win mag. I've also got one of the Stealths (push feed) in an A-2 stock that is under .5 moa @ 200 yards. Heard similar results from many on these rifles.
Not that familiar with Savage but have heard good things about the heavy barrels as far as accuracy goes. Daughter has one of the kid's .22 with the accutrigger. Seems to do a decent job. I've not had it apart to see about adjusting it. Seven year olds don't need a 1.5# trigger.