Savage can be very accurate out of the box. However, so can a Remington. The issue I found with two Remingtons I bought new about 4 years back were their triggers. Once my gun smith worked them over, they shoot like a Savage. Remington really took some hits back in the day on their triggers. This caused them to make their triggers Lawyer triggers. I had a 6MM BDL I bought new back in 1981. It had a nice trigger on it and I adjusted it lower to about 2 pounds pull weight. But these last two 700s I bought in 2006 and 2007. The one I bought in 2006 was an ADL Synthetic in 22-250 and the other was a 30-06 SPS I bought in 2007. Both weren't too bad out of the box, but both had 5+ pound triggers. I tried to adjust them but they both had a lot of creep when I got them down where I wanted them. And this creep was not consistent. One time it would be a crisp let off and the next it would be so sloppy I had no idea when to expect it to go off. My accuracy actually got worse after I lightened the pull weights instead of better. I took them one at a time to my trusted smith and he did a trigger job replacing springs and stoning the trigger and sear and got them both down to about 1.5 pounds with a very consistent, crisp let off. Now both rifles shoot very well. The 22-250 with a proper hand load will shoot less than .5 MOA if I can do my part with these old eyes. The 30-06 is less than MOA with a good load and me at my best. Also, if you ever want to spend some extra cash and really fix it up, the Remington is a very inheritly accurate action due to its rigidity and its super fast lock time. The 700 family of actions, 721, 722, 725, and 700 were all designed by Remington Engineer Mike Walker, who was also a bench rest shooter. Again, don't sell the Remington short because of a lot of media hype and other peoples limited opinions.
Oh Yeah, Forgot to mention, Remington has a new trigger that is safer than their old one and is user friendly for adjustment now. I think it's called the X-Pro. They had problems with them at first and now have improved them.