I’m looking at both in .308 20” barrel. Is one more inherently accurate with different ammo?
I want it for shots out to 500 yds for both target and hunting.

I Would go with the Bergara or a tikka varmint.
I am not a savage fan

I can't speak to the Savage, nothing against them just don't own any. I have a couple Bergara Ridge's and my friend has an HMR in 6.5CM. All of them will shoot easily under an inch with his HMR around 1/2 inch (he's still working on finding his ideal load but lots of promise). Since they're Rem 700 clones lots of aftermarket options. The triggers are good right out of the box and TriggerTech drops right in. Be patient with accuracy, barrels seem to like some rounds through them before groups tighten up. The 2021 Wilderness series is supposed to have a fluted bolt. I wouldn't hesitate to buy another.