The .45 3-1/4" was never a "Sharps" factory chambering however there were some Sharps rifles turned up with 3 1/4" chambers, notably .40, .45 and .50 calibres. At that time, Winchester actually chambered a .45 3 1/4" ctg. loaded with lighter bullets, same as the British Express ctg. They even used the same brass, I think. Winchester brought the .50 3 1/4" round out actually after Sharps closed their doors.
Other gun smiths or shops, possibly in St. Louis, re-chambered existing rifles to the 3 1/4" case. Fruend (sp) was one-such gun smith.
As far as comparing with the British .450 Express, the express was loaded with light weight, 270 to 300gr. bullets normally, while the 3 1/4" chambering in Sharps rifles were usually loaded with heavier, 500gr. and up, bullets, just as the long, 2 7/8" Sharps ctg. in .45 was loaded.
The Sharps 2 7/8" ctg. was called by what was loaded in it, which even happened to be 120gr. of powder and a 550gr. bullet, ie: .45/120/550. It did not need 3 1/4" to load 120gr. powder.
I also had a Remington RB in .45 3 1/4" chambering.

Loaded with modern powders & in a lever action rifle, the .45/70 will exceed what the 3 1/4" case (British or American) could do with black powder, with any bullet weight.