the 444 is just a bigger 44 mag case you will have better luck with the 45/70.
I guess that makes the .45-70 just a bigger .45 Colt case.
I was recently choosing between the .450 Marlin, .45-70, and the .444 Marlin myself. I reload, so I wasn't too concerned about availability of ammo on the shelves. I looked at the specs for the different rounds and saw that any of them would do everything I wanted the rifle to do so that was a toss-up.
I wound up buying a Marlin 444 with 24" MG barrel because it had a straight grip Monte Carlo type stock with pretty wood.
It has plenty of power for me, and with a Williams peep sight I can put five 265gr Hornady FP bullets through the same ragged hole at 50 yards.
If magazine capacity matters, the Marlin 444 holds 5. The .45-70's and .450's I looked at only carried 4 in the magazine. That wasn't a real concern for me, just something I noticed.