I shot the .45-70 LEs for at least 4 years, and they shoot and group well. I dumped a nice buck at 220 yards awhile back with the 325 gr. Personally, I'd opt for the .45-70. Ammo, components, etc. is much more available, and I don't believe the .444 can do any better. In all fairness, I've gotta say the .444 is on my "next to build" list along with the .500.
It sounds like you don't handload, so I'd say go with the LE's, Buffalo Bore or something fairly hot to compensate for the drop.....and....shoot it and shoot it and shoot it so you know where it is hitting. With either one, you're dealing with a big rainbow. You're not going to poke a rifle up at 250 yards, lay the crosshairs on the shoulder and knock the deer down. You're gonna kick snow or dirt up under his belly. The two calibers will knock them dead at 300 yards, but you have to do your homework and learn them.
Pete