I have owned a 505 Gibbs (actually it belonged to my father, but I shot it he didn't). I currently hunt with a 500 Jeffery Improved and a 500 A^2. All the 50 caliber rifles dramatically outperform the lesser big and heavy medium bores by a significant degree (there is no comparison between either of your 50 caliber choices and a 416 Rigby). There is also no discernible difference on game between a 505 Gibbs and a 500 Jeffery, if you are using roughly the same bullets and velocities that is ie not comparing solids to softs, etc. When I hunted with a Gibbs we loaded it to ~ 2400 fps with IMR4831 powder (if I recall correctly it was a many years ago). I currently load my 500 Jeffery Improved to ~ 2370 fps with 570 gr, 2450 fps with 535 gr and 2320 fos with 600 gr Woodleighs. By the way, there is NO need to use any other bullet than a Woodleigh in a 50, as their performance has always been satisfactory (actually far better than satisfactory). I keep my 500 A^2 loaded to ~ the same pressure levels as my 500 Jeffery Improved, and it runs 570 gr pills at 2220 fps, and 535 gr at 2300 fps.

Regarding recoil. I do not know what a "slow push" is! None of these rifles "slow push". If your 500 is properly stocked and fitted to you, which a properly built custom should be, I will tell you that you should NEVER get a sore aching shoulder before you get a splitting headache. Actually, my shoulder doesn't get sore ever with the 500 Jeffery improved (unless I do something very stupid like hold it off my shoulder when I fire it). My 500 A^2, which is a bored out Ruger M77 MkII RSM, doesn't fit me too well and has a bit more felt recoil, but it is fitted with a good pad and that tames it considerably. The lighter caliber rifles I have shot that weren't pleasant (my friends 338 isn't really one of them but is does have a nasty stabbing recoil) all suffered from the same two basic problems.
1.) Poorly fitting stock shape
2.) Piss poor or non-existing recoil pad.
Addressing one or both of these issues has tamed these unpleasant shooting 30-06s, 7mm Rem mags, 375 H&H, 300 Mags, etc.

My 500 Jeffery Improved weighs just under 11 pounds with scope. The 500 A^2 is about the same. I don't notice the weight when I carry the rifle slung over my shoulder (well padded sling) or in the so-called "Africa Carry". It can get heavy if one is carrying it for 30+ minutes in their hands though. The 416 Rigby weighed for reference 10 1/2 pounds (same big action). I hardly think you would notice the weight differential.

By the way, neither the Gibbs or the Jeffery are in any way short on case capacity. The Jeffery has ~ 15 gr more capacity than the 500 A^2 and the Gibbs has about 20 gr more capacity than the Jeffery. For me IMR4350 has been the powder for the Jeffery (to provide an idea on what burn rate will fill the case nicely).

Other than that I cannot add anythinh (not sure if I did anyway) over what 500nitro has already stated.

Scott