I'm a .375 fan, regardless of the head stamp. If we consider that a ballistically optimum barrel length is on the order of 28", we accept that we'll be giving up velocity with a barrel length of say 20". The question is how much, and what will the effect be on practical considerations of field shooting and bullet performance on live targets. The .375 will be more forgiving with respect to velocity drop than a smaller bore, although less forgiving than say a .458 or a .50. Of course achieving .375 velocities with a .458" or a .510" slug from a rifle of reasonable weight is a study in broken gun stocks, broken clavicles, and detached retinas (and the chance to end up starring in your own youtube video like those skinny guys from Accurate Reloading shooting the .577 Tyrannosaur or whatever it was that propelled them across the shooting booth).
Having shot and loaded the .375 Ruger in the Alaskan rifle enough to form an opinion, it would be my top choice off the rack, short, dangerous game rifle, or for that matter a general purpose big game hunting rifle for use where dangerous game might be encountered. In some (small) ways I found it preferable to my custom .375 Ultra Brno 602 that set me back enough to buy 3 Alaskans, and I dare say had it been on the market, my Brno would have become a .460 G&A. I am less excited about the latest version brought out by Ruger, although the muzzle brake could be unscrewed and properly used as a sinker when fishing, and the hideous laminated stock could be simply replaced with a quality fiberglass stock, although this represents a significant increase in the cost of the rifle.
When handloaded with due care, the Ruger Alaskan will shoot better than MOA, which makes it about 8X more accurate than need be, considering the size of it's targets. Game bullet choices for the .375 covers the entire big game spectrum, from up close and personal to reach out and touch. The selection of .375 bullets is actually better than those available for the .338, as the .375 is intended for game the .338 never was, and many of the newest .338 bullets are the match type for extreme long range use in a .338 Lapua, .338 Edge or .338-378. Thus whatever you favorite .338 game bullet might be, a version of it will be found in .375. I've never encountered any difficulty in finding components for the .375 Ruger, and of late, C-FBMI resolved any potential or imagined brass shortage of brass with his discovery that .300 Winchester brass can be fire formed in the Ruger to produce a slightly belted .375 Ruger. By all reports this hybrid brass feeds without issue, as the brass ahead of the web expands nicely to mirror the chamber.
All of these things are interesting tidbits, but the fact of the matter is that if you have a .338 rifle that has served you well and that you are confident using,there probably isn't much to be gained by switching up to the .375 unless African hunting is in your immediate future. A .338/250 or a .375/300 of similar design, impacting at similar velocities, will be indistinguishable to the bison.