You'd probably have to go with the 38-55. The 375 was chambered in the big bore rifle which was beefed up to handle the pressures of the 375 . The 38-55 can be loaded up pretty good and right on the heels of the 375 but at lower pressure. WHere are you finding a 38-55 barrel? I wouldn't mind that conversion myself. You can get a new winchester in 38-55 for around 350-375.
Hunter is right, don't put a .375 WCF barrel on a regular M94. You'll love the .38-55 anyway. I had mine rebored by Ackley in the 1970s and have had a great time with it over the years. With safe but powerful loading data available from Accurate, Lyman and Hornady you can make the old round into a great hunting cartridge. The only potential issue is the bore diameter, the classic .38-55 bore is ca. .378". Sometimes this won't handle jacketed .375" bullets well, but mine does. If you have the choice, specify a .375" bore. Have fun! :-D
I put in my vote for the .38-55. The only advantage I can see to the .375 is if you don't reload and can find some of the old 250 grain bullets. Winchester dropped them pretty soon after they began to manufacture rifles for the caliber. I guess "big game hunters" didn't cotton to the caliber without a belt on the case. Otherwise, .38-55 brass is easier to obtain, and it really shines with cast bullets. You can essentially equal the power of the .375 with lead bullets, if you have a 26 inch barrel.
A forum community dedicated to the great outdoors and hunting enthusiasts. Come join the discussion about hunting, fishing, survival, archery gunsmithing, optics, reviews, accessories, classifieds, and more!