You don't specify caliber or intended use, but I asume you want something bigger - possibly in a magnum to stretch your distances even farther? I would stick with the Savage. Seems to have the best record for "out of the box accuracy" claims.
Remington is still spotty. I would avaoid the SPS lines as their barrels are hit or miss for accuracy. I have limited myself to only recommending their high-end rifles, but even that is backfiring on me. I pushed a good friend wanting to get into LRH to buy a new Sendero II in 300 RUM. It might be a shooter, but who knows? Too many problems right out of the box. It was purchased new through a local gunsmith. First problem, was the the X-pro trigger would not adjust below five pounds. It was sent back to Remington nearly five weeks ago. They won't talk to the buyer directly, but will only work through the retailer. The gunsmith/retailer has faxed in a copy of his FFL three times and yet Remington says they never received it. Won't talk to him either.
Frustrated, my friend "borrowed" a trigger from another model 700 he owned and went to break in the barrel. He found the new rifle had feeding issues. It jams half way through the chambering cycle. Looks to be a problem with either the follower or the feeding lips. At this point, he is not sure what he wants to do. Regardless, I feel Remington should never let a $1,200 rifle keave their factory without checking some basic operastions.
Not trying to rant, but I am feeling a little burned by Remington at this point. Not my only bad experience with a new rifle purchase from them. BTW- two of my custom rigs are built on 700 actions, so not stumping for another mfg - just surprised with recent QC issues at remington.
On the other hand, I bought a cheap little Savage Edge in 243 for pradator control last year based on recommendations from this site. This little gun shoots every bit as good as my model 7 wearing a custom Brux barrel. Not bad for $325 American.
I have also had good luck out of the box with Browning A-bolts. I have owned two and bith shot lights out. I have also heard good reviews on Tikka, but even those seem to be a little mixed lately. Never heard of a Sako that wasn't a shooter (except their A-7 blunder, which was mixed in terms of accuracy).
I'm sure others will chime in as well. Good luck in your search. Let us know what you end up with.