While I haven't had my 375 BB long enough to hunt with it yet (this fall) I have worked up loads from Paco Kelly's reads, and am now pushing chrono'd loads of 250gr bullets at 2135fps from the 20" barrel. Now when you read the Hodgdons manual shows the 30-06 pushing a 250gr load at max of 2200fps from a 24" barrel, it puts its power into perspective.
These loads have been carefully worked up .1 gr at a time and have zero over pressure signs. They are safe in MY gun but don't know about anyone elses. I'd use this load on anything on this continent out to 200yds with the exception of a brown bear, and I might limit it to 100. But since I'll never hunt brown bear, that is not an issue for me.
But like ramrod said, the levergun is fast handling and built for the woods. By the way, in factory loads, the 38-55 is nowhere near the 375 Win. In handloads, and in the RIGHT RIFLE, the 38-55 can match the 375. Both rounds are like comparing factory loads of 45-70 to the 450 Marlin.
It is like apples and oranges to compare a 375 H&H bolt to the 375 Win lever. If you want a big heavy slug from a woods gun go with the 375 and reload. Otherwise get the 444.