Define your criteria for measurement, please
There are three types of ballistics, internal, external and terminal.
Internal ballistics defines what firearms can launch the 44 Mag or 45 Colt with what energy levels and throw weight. This is basically where the muzzle energy arguments take place. This is usually pretty easy to determine from loading data, but does nevertheless produce a lot of heat.
External ballistics is concerned with the bullet path between muzzle and target and aside from bullet drop and how far you can shoot accurately has produced little heat.
The king of the heated argument is terminal ballistics. Aside from the indisputable fact that the 45 bullet is 5% larger in diameter, 10.5% larger in frontal area and 16.2% heavier for the same profile the performance on the target at whatever bullet construction, velocity, spin rate and distance will never be settled (in my opinion) because there is a great deal of overlap in the abilities of both rounds.
You MIGHT be able to get a definitive answer on which is better against an easily reproduce target like a steel plate hit by a specific weight bullet from either cartridge, but on a target as variable as even any one specific game animal, there is too much variability in the target to ever get a sure conclusion.