Yes, both the 444 Marlin and the 44 Rem Mag are .429 caliber. I'd suggest keeping with jacketed bullets in the 444, and not any of the lighter soft stuff meant for pistol velocities.
Now, stating this upfront, I've never shot, nor hunted with a 444. I have some limited, successful field experience with the 44 Mag. I would guesstimate that anything under 240gr is simply begging to be a disaster on game. The 444 was designed to toss the heavier stuff with umph that the 44 Mag just can't, not turn a .429 bullet into a ridiculous range stretcher.