If you're going to send the Remmy in to LRI to have the action trued, get a decent barrel installed, side mounted bolt release and AR15 style extractor installed go with the Remmy, after that if you're getting it for hunting you'll be good to go; if you're getting it for precision shooting ditch the Remmy stock and get a chassis, or if you want to invest further into bedding and a DBM get a Manners, or McMillan, or a Foundation stock.
If you want a rifle with a decent barrel, side mounted bolt stop, and sliding plate extractor out of the box get the Bergara. I used to get Remingtons exclusively for most of my life but there came a time when I was fed up with their shoddy manufacturing and QC and having to chase good money hand over fist after bad spent money to fix what should have been done at the factory, and to get the upgrades that would make the rifle closer to what others provide straight out of their shop.
Don't get me wrong the Remington is a great rifle, after all it is being copied, and trued and upgraded by shops around the world with its footprint but the manufacturing has taken a nose dive. I'd go with the Bergara, if you end up not liking the stock you can always drop it in a KRG Bravo chassis for $349.
Depending on your budget, you might even consider a build based on a Bighorn Origin, PROOF Research steel pre-fit barrel, TriggerTech Special, in a KRG Bravo and I'm sure you would end up enjoying the result. It all depends on your budget, intended use, and how soon you want to get it finished in hand. The advantage of a build is that you can take your time to acquire all the parts you need and want and get exactly the rifle you want, even if you could not afford to drop that much cash at one time. If you want to get to shooting right away on a limited budget though get the Bergara.