I own and hand-load for both.
My 8x57mm Sporter is a Vz-24 with a 22 inch Douglas barrel. It likes 200 grain Nosler partitions loaded up to 2,600 fps (53 grains of H-4350 and a Fed mag primer using old Norma brass.) It will shoot a 5 shot group under 1/2 MOA if I do my part.
The 338 federal was an impluse buy.... a Ruger Frontier Rifle with a 16 inch barrel....
It is one of the least accurate rifles I have ever owned..... the best group with a 200 grain bullet comes from using 49 grains of H-335, federal brass and a Standard match primer. It will push a 200 grain Speer spitzer (it hates partitions) at 2,550 fps from the short barrel. While impressive velocity from a carbine barrel, the two inch groups (the best this rifle can do) leave somethng to be desired....
So in theory the 338 fed might be a little more zippy from the same length barrel, BUT it has a couple of porblems. It is a short case /neck and you can't load the COL too long... And the short neck seems to be giving me fits in the accuracy dept.. Plus it seems like the loads the it likes are pretty hot and brass life is pretty short.
The 7.92x57mm is not quite as efficient, but the slightly longer neck helps with accuracy. And you do not have to hot-rod your loads in the pressure dept either...
The down side being bullet selection and a longer over-all case length which requires a longer action.