charlessala: You went out and bought my favorite rifle. I absolutely prefer the Winchester 94 over the Marlin. I just prefer the styling, looks and feel of the Winnie. I've had a marlin in 444 and although it was a fine rifle, my preference is for the Winchester. I am still looking for another one with the 20 inch barrel.
To answer your questions. The Winchester will stand up to any commercially produced ammunition in the 444 caliber. The Winchester Big Bores in 444 are/were re-designed with a slightly heavier frame for just that purpose. Winchester would never market and sell a rifle that would not handle the pressures of the cartridges it was designed for. Period. Do not worry about your 444, it will eat anything made for it and ask for more. Nobody out there who makes commercial ammo for the 444 'overpressures' the loads. They are all within SAAMI limits, no matter how hard they wallop.
300 grain bullets in the 444 (430 diameter), whether jacketed or cast, have a higher sectional density and greater penetration capabilities than the same weight bullet in a 458 diameter. For the 45-70 or 450 Marlin to match that section density and penetrative capability, they would have to go to a 400 grain bullet or something close. In this regard, for anything on this continent that you would need that kind of power for, the 444 is my choice. You can go all the way to 40 grains in the 444 - to match that in the larger 45-70, you have to be up to a 500-550 grain bullet - something you can't really shoot from a lever.
For as many problems as the micro-groove rifling has caused me when trying to reload plain based cast slugs, and for as often as I prefer not to have that style of rifling, the micro-groove rifling is not inferior to the ballard style with a faster twist (say 1:20), unless you intend to shoot plain based cast bullets. The micro-groove rifling will handle any jacketted or gas checked bullet very well. Yukon Jack gave you some good advice about visiting the BearTooth Bullets web-site for information on their testing results.
You may wish to consider reloading, even on a smaller scale for just that one cartridge, the 444. At least two of my reloading manuals, as well as the BearTooth reloading forum, provides numerous load data for the 444 to bring the 300 grain bullet to 22-2300'/sec. The same weight bullet in the 45-70 or 450, at the same velocites, seems to pound you much worse on the recoil side. And, although you can get the 45-70 in a 300 grainer that will match those velocities, or come close to them, most of the 300 grain loads for that caliber are 3-400'/sec slower. Somebody out there makes a 300 - 350 grain 45-70 they refer to as the Hammerhead. A 300 grain 444 at 22-2300'/sec should probably be called the SledgeHammer from Hell by whatever the poor critter is on the receiving end.
In the early days when the 444 was limited to 240 grain 44 magnum bullet offerings from the factory, it was limited - but no longer. Heavier bullets in the 265, 270, 300, 325, 350 and 405 grain weights for the 444 cange that equation beyond all expectations. Also, with the 444, you need not drive a heavy bullet to max velocity to get it to perform. One gun writer penned that driving heavy 44 magnum and 444 Marlin (300 grains or better) to higher velocities is not necessary, as the heavy bullets in that diameter seem to peform all by themselves. Interestingly, no one has ever chronographed the heavy bullets, in any caliber, beyond the muzzle, yet extrapolate velocities and trajectory through computer algorithms. I'm just willing to bet a 12-pack that those heavies neither lose that much velocity or penetrative capability at distances out to 2-300 yds, especially as you narrow the bore a bit. I think they just carry incredibly and that momentum and weight continue to combine that capability, even much farther downrange than ever thought. A good exercise is to try and recover some of the heavier hardcast or jacketted bullets from a sandback 2 - 300 yds downrange, and see how far you have to dig to find them. That will give you a good indication of impact possibilities on game at those distances. They tried that over a hundred years ago with the 45-70s with the 500-550 grain slugs at maximum distances - 3500 yds, as I recall reading, and had to dig deep, real deep to recover them.
As to the best barrel - if your Winnie sports the short 20 inch barrel, it probably carries the micro-groove rifling with a 1:38 twist. As before, this barrel should shoot any factory 300 grain offerings, whether jacketted or gas-checked, accurately. If yours is the 20 inch barrel, you have a real sweetheart. I advocate reloading only to save yourself the money you would spend on buying enough factory fodder to really shoot that baby like she wants to be shot. Also, if when you clean your barrel after shooting, if you get a lot of copper residue or fouling, you may be able to benefit from barrel lapping, and I would check out the BearTooth website for information on that process - or, just shoot the schmidt out of yor 444 until your barrel smoothes out a bit. It's good fer ya.
If you feel you do not attain the accuracy you need from your particular rifle, look to a sight change. The Winchester bead front sight and those half-baked 'Buckhorn' rear sights they provide do little to enhance accuracy. You might have much better luck with a blade fron sight and a rear tang sight with a peep aperature. This sort of a set up gives you much better visibility and, from my perspective, accuracy.
You need little education on these issues my friend. You have demonstrated quite a bit of knowledge already - more than enough to ask the kind of questions you have posed.
In all honesty, no animal is going to know the difference between either of the 3 calibers you mentioned. I would not spend the money for a larger bore, because anything you want to do on this continent you can do with the 444, very effectively. I can readily understand your preference for the Winchester - I would use it to your heart's content and never once give a thought to being undergunned or having made the wrong caliber choice.
Hope this helps. Mikey.