I've wondered this myself over the years and it's impossible to get a straight answer from the Internet Gun Community. I'll attempt to cut thru it and give you the best answer I can.
In terms of power, they're about equal, but if you're gonna go above the 14k PSI limit for .45 Colt then you're stuck with a Ruger or a BFR for revolvers, for .44 Mag as long as it's chambered for .44 Mag, you can shoot .44 Mag from it. I have a .45 Colt Redhawk that also shoots .45 ACP... it's probably my favorite revolver and I've read that they can eat 50k PSI loads all day.
I've been trying out loads for the .45 ACP to see how much I can push it. Right now 5.4gr of Bullseye will push a 225gr lead bullet to 840 fps, that's with a decent jump to the throat and the gap sucking some energy. My goal with the .45 ACP in the Redhawk is to get to 1000 fps with a 230 grain jacketed bullet and I see no reason the Redhawk can't handle that.
Hot .45 Colt tho, I have no need to load to 50k PSI even tho the Redhawk can take it. If I want more power than 14k PSI, I use published data and IDK of any published data that goes much above .44 Mag pressures.
Case life with the .45 Colt... it depends on the brass you use. Apparently Starline has tested and advertises that their .45 Colt brass can handle .44 Mag pressures:
https://www.starlinebrass.com/45-colt-brass
Other companies I severely doubt their .45 Colt brass was built for anything more than 14k PSI.
Accuracy I can't speak much to as I've never shot .44 before. I can say that with standard pressure .45 Colt loads, the case volume is so large that it can cause inconsistency with the power burn and ignition, but if the .45 Schofield case is used, given the case volume is less and the amount of air is reduced, it shoots more consistently and accurately. With higher power loads, I see no reason the .45 Colt can't be as accurate as .44 Mag.
In a rifle I see no difference between .44 and .45 Colt, but I've been trying to find out how well .45 Colt levers cycle when using bullets that weigh 300 grains or more as those would be longer than normal and I can't get a straight answer on that either. With .44 Mag, it seems they're able to cycle anything from 200 grain loads to 300+.
What I like about .45 Colt is it can shoot the same bullets as .45 ACP, so when it's panic time your available selection is greater. I also like that if I want to make a load that uses two round balls, I can use the Speer or Hornady muzzleloader balls that I already have for my .44 percussion revolvers. The balls are also about 20gr heavier than the .433 balls, so that's an extra 40gr of lead being put down range with each trigger pull.
For a revolver, especially if you get a Ruger that's able to shoot .45 ACP, there's a lot of reasons to get .45 Colt. For a lever action, IDK.
