It was the only modern big bore lever action available for a short while until Marlin re-introduced the 1895 in .45-70 in 1972. The .444 came out in the 60's, was popular for awhile, yet despite little fanfare over the years and exitement today with all the new fangled cartridges, it is still around. And because some think bigger is better, it's always been in the shadow of the .45-70.
Load it right, touch off a round or two, and you'll realize its no slouch. It drops deer in their tracks, at least that's been my experience.
I've been shooting mine since the early 80's. My rifle likes the 265 gr. Hornady. I have never tried the new Leverevolution rounds in my MicroGroove barrel.
I think where the .444 Marlin suffers is lack of more factory bullets since it shares the same diameter (.429) with that dinky pistol cartridge; the .44 Rem. Mag. Many .429 bullets are too light or are designed for pistol velocities, not rifle velocities. But, when Barnes made a heavy jacketed .429 for the .444, or when using the excellent Hornady 265 gr. FP Interlock, which I've used exclusively, I've never experienced any problems.
Over on the MarlinOwners forum there is a group dedicated to the .444 Marlin with lots of good info.
This is a pretty good read on the rifle and cartridge: