378 Weatherby-300gr bullet @ 2925 ft/s and 5699 ft/lbs
460 Weatherby-500gr bullet @ 2600 ft/s and 7504 ft/lbs
Very impressive, however getting back to why they are not liked.
Excessive recoil-few can handle them and shoot them well, most can't, resulting in follow up's, wounded and lost animals, not due to lack of ability of the cartridges but due to bad first shot placement as a result of the recoil.
Long recovery and reload time for the second shot due to excess muzzle lift(recoil).
In an attempt to manage the recoil, many are fitted with muzzle brakes-I hate them and have yet to meet a PH who likes muzzle breaks on a DG rifle while guiding a client using one.
Excessive speed again resulting in wounded animals. Download them to a sensible velocity and you have a wonderful African rifle. Then remove the brake if fitted as you will no longer need it.
Excessive speed in DG cartridges actually gives you less penetration than slower speed. You do not need more than 2400 ft/s in a DG rifle if you use heavy for calibre bullets. A 500gr solid bullet at 2400 ft/s will out penetrate the same bullet doing 2600 ft/s.
They are wonderfully strong rifles and actions, well finished, have excellent triggers and although they have push feed actions I have yet to see one not function as intended, however in factory form they are loaded to high pressures and speeds that are not needed in Africa.
I well remember a 18 day hunt with Spanish client who arrived in camp with a brand new 460 Weatherby that he had ordered from the Weatherby custom shop. The stock, finished with some shiney farnish, shone like a mirror and although it had one of the best figured pieces of wood I could just not understand why the stock had this shiny finish. He had quite a few animals on his wish list, including elephant, 2 x buff, sable, lion etc. This rifle quickly started beating and battering him up as the safari progressed and at one stage he used one of my 375 H&H rifles on his plains game animals as he could no longer endure the punishment dealt out by this power house with it's full power loads.
At the end of the safari, he presented me with this rifle, which although I thanked him profusely for, declined to take as I had no need or use for it. I use a 500 Jeff as a back up rifle on DG and have the utmost confidence in this rifle. This upset him and he insisted I take the rifle.
Long story short, I eventually took the barrel of the Weatherby(in those day's only the barrels where licenced in my country and if he took that back with him there would be no need for licencing etc.) and kept the stock and action.
It sat in my safe for a long time until I eventually gave it to my gunsmith who fitted a 30 1/2 inch 338 Lapua Magnum match barrel. Converting it to a "long range fun gun", for lack of a better description. He at the same time god rid of the shiny finish on the stock and did a London oil finish on it. It now has the most beautiful stock of all the rifles I own. It shoots very well and I still own this rifle.
No issues with Weatherby rifles, rather with the full power loads they come with. Down load them with heavy bullets to a sensible velocity and get rid of the brake and you will have a wonderful DG game rifle.
But my 2 cents is they are purty POS because 1. too much head space to get out close to the lands and groove when seat bullets 2. burn alot of powder for some extra speed and extra recoil 3. kill no better than non weatherby similar cal. 4. not control rd feed 5. overall i dont find any that are super accurate the radius shoulder design that isntt conducive to best accuracy. 6. all that extra power eats up brass cost 7. cost more to feed a webby. 
