Dino - if the 40-44 is a 44 magnum necked to take a 40 caliber bullet, then you are talking about a cartridge that is in the 38-40 power range. The 38-40, 44-40 and 45 Colt are all based on the same cartridge case, the 45 Colt. The 38-40 is necked to take a .400 diameter bullet and the 44-40 is necked to take a .427 - .429 bullet. The 40-44 is based on a (smaller capacity) 44 magnum case.
In modern handguns and rifles the 38-40 can be loaded pretty hot, and was loaded to some pretty hot levels even in the old days. My older Lyman manual shows that in a 20" rifle, the 38-40 could be loaded to 1980'/sec, with a 180 gn jacketed bullet over 24.6 gn of 2400 powder, or loaded to 1904'/sec over 26 gn of 4227 powder. This new 40-44 Woodswalker will probably do about the same, although I don't think you will be able to stuff that much powder into the 44 magnum case once it's necked down to 40 caliber.
I dunno, everybody is trying to come up with new cartridges these days - apparently the old ones that were good enough for the larger game we had 'back then' aren't good enough for the game animals we have now and I guess we just gotta have more magnums to do the job. Sure!
I think that if I had the choice twixt a 40-44 Woodswalker in a single shot pistol or a 38-40 set-up in a new rifle or carbine and a handgun to match that caliber I would be in fine shape for hunting most anything ('cept really big and mean stuff) with the 38-40.
Put it this way - Elmer Keith once wrote about the 38-40 cartridge and how the 'soft' factory loads deformed and skipped off a bull's head when Keith had to fire to stop the bull from charging. He wasn't too complimentary about the factory round from a pistol, but immediately after he fired that round, he put two of his handloads with hardcast swcs right through the bull's skull, killing him. If 38-40 handloads can do that with a charging bull, that's pretty good.
As I mentioned, you can handload the 38-40 very respectably from modern firearms, but if it's a Woodwalker ya'll want, then....... HTH. Mikey.