Remington or Savage
I own 2 Rem 700 "police" and they both shoot great. (1/3 moa) All I did to the 308 (LH) is rechamber the 20 inch bbl to "match" I also have a palma 28 in. bbl with match chamber. The other is a RH. Came in 22-250. added a Gaillard 28 in. barrel in 260 Rem for 350$. A chamber job is 200$. well worth it.
I used the 308 at two Palma matches in Albany NY (800, 900 & 1000 yds) and got my share of Xs. Did a sniper match in TX last year also.
I glass bedded the 260 with a friend (20$ job for the marine tex epoxy)
I know the Savages shoot great too. I even saw they came out with a detach mag on some models. Someone told me they have centerline feed. I'm looking into that. They didn't have any at "Sail" my local gun store when I went today. Their buyer is at the SHOT show in florida now. When he comes back they will get them in. The model is 14 I believe (hunting rifle) As soon as I know more I will post the info. A hi-cap mag would be great. I have 6 shot mag extensions on both Rems (18$ At Brownell's)
What I don't like about the Rem 700s is they come with a throat which is way too far. I loaded the 155 SMKs at 2.95 touching lands. The mag OAL is 2.80.
Bummer!

My match chamber is touching at 2.80 for the 155 SMKs and 2.84 for the 10 gram Lapua Scenars (154gr) I don't know what the Savage is like but if they make a centerline feed mag it soundls like smoother feeding.
I tried a Sig Blaser 93R LRS2 in 6mmBR lately and that is centerline feed on top of being a straight push-pull action. Smoothest thing I ever tried if you can afford it. I don't see why it's so important to be good out of the box. You get what you pay for. Any serious shooter that wants his rifle to shoot better will get something done on it (match chamber, truing action, glass beding and/or pillar bedding the action) The match chamber is the best improvement for your money. There's no free lunch. Don't forget to get a good piece of glass. As much bucks as the rifle price if you can. I have a 10X S&B on my 308 and it's not money thrown out the window I assure you.
Good shooting all.