I personally prefer the 44 because it delivers all any north american animal needs for a quick kill. 300 gr bullets have to be driven at about 1800 fps plus for good long range accuracy, which puts recoil up there with the hard kickers from such a light gun. I prefer a 280 gr LFN, loaded to 1500-1600 fps. For smooth feeding in both the 44 and 45, nose length has to be held a bit shorter than my standard .45, which is actually a nominal designation relating to space from end of ctg to end of cylinder. Nose length is a bit short of .45 for revolver bullets, and shortened from that a bit for these two lever lockers. An actual .4 nose will probably feed in any of them.
Bullet diameter must be large as will chamber smoothly for top accuracy, this to keep the bullet aligned while being fired into the rifling. The 44's tend to have tighter chambers, which is another reason I prefer it over the 45.
Maybe most important in making a decision is to stick with which ever cartridge you are now using, if you are using one of them for revolvers. It will cost a pretty penny to buy brass and dies for a new cartridge, and sorting brass is a hassle if these two should get mixed together. I've never personally owned a 45 for this reason, because I got a 44 first, compared brass, and disliked the idea of using a magnifier to sort them out by head stamp.