The .450 3 1/4 Express is a BP round, originally, just like the Sharps 3 1/4" case. The only difference is in factory bullet weights and actual ctg. case dimensions. I assume the difference in bullet weights is or was due to rifling twist and intended game and expected trajectoires. The Sharps rifles generally had 18" ROT's, seems to me. I di not know the ROT's of the .45 3 1/4"Express rifles. If you are referring to the .450Nitro Express, that is a different animal.
The Sharps case was never an "EXPRESS" ctg. and was intended to be a long range bison ctg., using bullets from 500gr. through 540gr., whereas the .450 Express, loaded with 270gr. through 340gr. bullets was intended for the plains game antelope etc. of Africa, I believe.
I assume both could be loaded to similar pressures if chambered in the same rifle.
I loaded an "Express-type" load for my brother for his .45 3 1/4" Shiloh Sharps, using Hornady 300gr. H.P. bullets over 62gr. Re#7. + kapok to fill the space between bullet anf powder. This load produced 2,200fps from hhe 30" bl. It also cloverleafed 3 rounds in 2 successive groups at 100yds for him, using the tang aperture and blade front sight. He shot one moose with this load, broadside at about 40yds. The bullet exited the off side makingva 1" exit hole. Both lungs were pulverized and no.meat was destroyed, except where the bullet centered a rib on the off side. The moose walked about 30feet and lay down, dead.
I do not know if this load would be safe in the British BP Express rifle. It was OK in his Sharps with it's large dia. BP firing pin.