I only own a 444p, but did a lot of research before deciding on .444 or .45-70.
The answer is they overlap a lot. From everything I have read, they overlap on elk too.
The one easier area to make a decision on is reloading. The 45-70 is easier to deal with there hands down. More recipes, more bullets designed to be fired in a rifle, more sources of brass, and more bullets designed to work with the OAL of the cartridge. On the other hand, the .444 is more versatile, but you have to work harder for it. You can load light plinking rounds, up to stuff that is on par with factory 45-70 (or even a little bit harder hitting). With 45-70, you can't really mess around on the lighter end of the spectrum, but you sure can play around with some quite heavy bullets. (range for .444 is from 200gr to 405gr for bullets with .405gr requiring a lot of know how to load safely. 45-70 is from about 300-525gr)
Neither is objectively better, but it is a pretty clearly defined line to choose around.
Factory ammo available? 45-70 has more options overall, but with the .444 I can go with the 240gr remington at the light end, and I can order a 335gr round at 3049ftlbs and 2025fps from buffalo bore. Their 45-70 in similar weights is a tad lighter on the ft-lbs and slower moving. Cor-bon, grizzly, and buffalo bore have both cartridges covered for some pretty insane ammo. If you want to walk into a store and find something in stock, 45-70 is a better bet.
The 45-70 lets you choose from more guns to shoot it from. If you are thinking marlin lever guns, you want the ones with ballard rifling, not the micro-groove rifling for 444, and probably 45-70 too.
They both have trajectories that want you to keep it under 200 yards.
As for hunting, the best I could put together was that if you wanted to hunt bigger bears along with elk, go 45-70. If you want to hunt deer as well as elk, go with .444. If you want to shoot your elk form farther away, go with a bolt action gun and an appropriate bottle neck cartridge.
ETA: some answers to a late post by OP
Then this brings me to another conflict in statements. A lot of guys tell me that the .444 Marlin uses .44 mag pistol bullets. But then I have guys who tell me that said issue was a birthing problem for the .444. I do know that Hornady's "Leverevolution" cartridges are designed with a rifle bullet.
The remington cartridge uses a pistol bullet. For a while, the best alternative was the swift a-frame .44 pistol bullet, which would penetrate well, but had too big a hollow point and would fragment the expanded petals. The hornady leverevolution and light magnum 265gr bullet is a rifle bullet. The cor-bon light end ammo uses the barnes pistol bullts, but they are solid copper alloy and generally stay a bit more intact than jacketed pistol bullets. Most of the heavy stuff in both calibers is cast lead. In .444 that what cast lead bullets that are easy to find won't come apart, but tends to have the cannelure in the wrong place for the .444 as loading hefty .44 magnum rounds at some point you need to preserve cartridge capacity so they design the bullets to be stuck further out the front. You need to find cast bullets that either have the cannelure in the right place, or have double cannelures. One for pistol and one for rifle.
Beartooth bullets is a fan of the .444 and has a number of good articles in their tech notes section on reloading for it with heavier bullets. They also sell a lot of cast bullets specifically intended to work with the .444 (with differing levels of effort required).
If you take a good hard cast lead 300gr projectile in 45-70 and 444 marlin, you can expect them to stay intact about the same in the same critters.
