Depending on your use for the rifle, if either of the two will do, I'd go for the FN over the Sako.
Typically, rifles chambered for the 338 are more compact and lighter in weight than 375's, so they are easier to hunt with. There's not much in the U.S. that you need either for except for the big bears. Either of the 2 cartridges would serve well in that capacity, with the 375 probably having a little more edge using the heaviest of bullets.
For elk, moose, caribou, or anything else here in the States, I doubt the animal would ever know the difference between the two. The 338 might be a little easier to tote over hill and dale for the shooter though.
If the FN Browning Mauser is in really good shape and doesn't have a saltwood stock, that's a really good price, and they are really fine rifles.