Litefoot: Get the 444P. Although you can use the same diameter bullet in both cartridges, which you can not do with the 45-70 and 45 Colt, the bullets for the 444 are designed for heavier loads, faster velocities and deeper penetration than the 44 mag bullets. You can shoot them in your 44 mag but, the 300 grain xtp for the 44 mag might not hold together as well or penetrate as deeply as the 300 grain bullet for the 444. Of the 44 caliber bullets, there are those plainly marked for pistol, because the skin on those is thin enough for the bullet to perform at pistol velocities.
The exceptions here are, of course, the flatnosed gaschecked cast bullets. Some of those in the 300 grain range serve both the 44 mag and the 444. Dropping down in weight a bit, the 265 grain Hornday bullet for the 444 is an excellent choice for large animals like Elk. One of our posters took a large cow Elk at 80 yds with the factory 240 grain 444 and others have done the same. I like playing with the 444 with heavy loads. Harpy makes his own 444 bullets in weights all the way out to 410 grains and they look absolutely gorgeous (his bullets, that is). I would like to approach him to see if he would be willing to sell some.
But, the point of all this is that you will not go wrong with the 444. You can't argue with the myth and history of a century old cartridge, and especially one that continues to perform as the 45-70 does but, the 444 will do the job on anything on the north American continent with the loadings offered from different manufacturers. And, if you like to handload, you can really brew up some incredibly accurate loads for that caliber. I would recommend you touch base with Harpy on this. Another fellow to touch base with on this is.......CRS is setting in......he is the one who casts out his own gas checked 335 grain loads - is it Lloyd (?) and throws them out with incredible accuracy.
I would ask some of the other 444 afficionados to jump in here and give you the benefit of their advice. Hope this helps. Mikey.
ps: although I have that one long barreled Winnie, I just put a down payment on a Timber Carbine. But to be honest, I'm looking at that one as though it is going to kick my butt, even if it is ported, but man, what a sweetie she is.