You guys are busy trashing Browning and BAR rifles, and I just can't agree with you. My BAR in 270 shot pretty darn well. Granted, it won't shoot as well as my bolt guns, but I got 5 shot groups into an inch with handloads (IMR4064). I'd probably still be hunting with it, but I got into reloading and wanted more accuracy and case life. And it was pretty heavy. Dad had one in 308 and it shot very well also with factory ammo, and gun weight finally got to him too.
Like I said earlier, if I was the OP I'd swap out scopes and check the mounts in the process. And, check to make sure that none of the screws in the mounts are protruding slightly into the action. If it protrudes too much, it'll keep the action from cycling once in a while. If it rubs the bolt just a little, but not enough to prevent the action from cycling, it could possibly be the cause of accuracy problems.
Browning makes a very high quality product, and I'd much rather have a Browning than anything Savage produces. Maybe if I shot F Class I'd feel different about Browning, but I'd still avoid Savage. To me, they are unattractive and rough. There probably aren't many Sako's in F Class, but who among you will swap your Sako for a Savage. Not me.
I am not saying that Savage isn't a good rifle. I just have no use for one.