I used to be the product manager for Sako at Beretta USA, so I know quite a bit about these rifles. They are tested to shoot within 1" at 100 yards, so they come with a MOA guarantee. Obviously, the ammo they use is SAKO, and they test them in controlled conditions, but they were among the first to offer such a guarantee.
The barrels are cold-hammer-forged, which in theory gives more molecular consistency in the metal. With today's steel, that's largely academic, but it's as good a method for rifling barrels as any other. The action has been changed from a push-feed (SAKO 75) to a controlled-round feed (85), which means quite a bit to some shooters who are worried about jams or working the action in awkward positions (this too is rather academic IMO).
The Optilock scope-mounting system is one of the best I've ever encountered, since the rings hold the scope firmly in place but without damaging the tube. I've traveled quite a bit with SAKO rifles and the zero never changed once I deplaned.
Triggers are adjustable, and depending on the model you get (they now import on-and-off Euro models) you may have one with a set trigger. Anyway, 2 to 4 lbs is the regular adjustment range, and I have never wanted anything better than a SAKO trigger adjusted to about 2.5 lbs. You can still feel the pull, but it's crisp and free of any creep.
The 3 massive locking lugs in the action make it strong and positive, so you never have to worry about hot-rodding your loads.
Bottom line: these guys have been making and optimizing rifles for decades, so you'll never have to worry about quality dips like with other companies that have changed hands/philosophy. Full disclosure: I don't own a SAKO because I rather shoot English vintage pieces, but if I had to buy a new bolt rifle I wouldn't hesitate to get one. I honestly can't think of a more reliable, accurate, steady piece of equipment than this brand. It will also turn heads in camp, since it's a premium product well known by connoisseurs. Enjoy it and get the most out of the venerable .375.