Do you have any preference about the make of pistol you will use for these magnum pistol cartridges? Choices are pretty limited. The only pistols produced in any quantities for the .45 Winchester Magnum cartridge were the Wildey and LAR Grizzly. The Wildey is still in production, but the Grizzly isn't, though for now it is still pretty easy to find used Grizzlys if you do some looking. For the .50 AE cartridge, the Desert Eagle is by far the easiest .50 AE pistol to find. LAR did make some Grizzly's chambered in .50 AE before production of the Grizzly pistol ended, but the total number of .50 AE Grizzlys made was much lower than the total number of .45 Winchester Magnum Grizzlys made, so the .50 Grizzlys are much less common than the .45s.
AMT/IAI (the makers of the original magnum semi-auto pistol, the .44 automag) also made the Automag IV and V pistols, which were chambered in the .45 Winchester Magnum and .50 AE cartridges respectively. However, not very many of these IV and V series Automag pistols were made before production ended, so they are pretty hard to find. I wouldn't recommend them in any case. One of the main reasons they went out of production so quickly was because they had a reputation for being unreliable.
So if you prefer a Wildey or Grizzly pistol go with the .45 Winchester Magnum, and if a Desert Eagle suits you go with the .50 AE (you might be able to find a Grizzly in .50 AE too). If you decide to go with a Grizzly, consider yourself warned about the magazines, which are both expensive and becoming increasingly difficult to find.
