The slower twist rate would almost certainly limit the bullet weights you could use in the .444 and using lighter weight bullets (300 grains and under) would gain little (if any) advantage over the .44 Magnum. In fact, due to the increased velosity bullets of 240-265 grains might even perform poorer than in the .44 Magnum by overexpansion and under penetration.
It would "limit" you to 355 grains or so. If that isn't heavy enough, a larger caliber/cartridge would be a better choice than a heavier bullet in the 444. Period.
I agree that certain bullets may perform worse at the higher velocities because they were made for handguns. But a 270 gr Speer or 300gr Speer will flat out amaze at 444 velocities. They are bonded, 2200fps is completely attainable, and the last 300 lb bear I killed with the 270 broke both shoulders and still retained 92% of it's weight. Still have the bullet, which ALMOST came out the opposite side hide of the bear.
The 300gr bullet I used fully penetrated both sides and left a HUGE wound channel. MOF, both Speer bullets left larger wound channels AND penetrated deeper than bears shot with 450 Marlin via 350gr Hornady XTPs................
