if you are choosing between just those two, i personally would take the .500 jeffery hands-down over the .505 gibbs
the jeffery was more popular because of its feeding, extraction and muzzle velocity.
then hemingway made the .505 gibbs famous by featuring it in a short story. otherwise it would have been pretty unknown compared to the .500 jeffery IMHO.
you can load the jeffery with 535 gr woodleighs to over 2500 ft/sec with 24" barrel; or a 570 grain to 2350 fps; or a 600 gr to 2250 ft/sec. these loads will flatten anything that walks on land in this era.
i am presently building a .500 jeff on a remington model 30S action.
i looked at the 505 gibbs and rejected it.
if you decide on the gibbs, i would recommend the demoulin imperial magnum action: it has a huge diameter bolt which will handle the gibb's extra-wide case-head diameter. conventional diameter bolts would have too thin a metal lip on the face of the bolt, where the lip it surrounds the base of the cartridge case for controlled-round-feeding.