The 378WBY is sort of an improved 416 Rigby, strengthened, solid bottomed, belted and will handle much higher pressures. All of the 378 based cartridges will hold 120gr+ powder and are real brutes.
I shoot and reload for 300WBY and 340WBY, which most people consider grossly over powered. They can hold 90+gr powder.
WBY manufactures the 378 group rifles with a muzzle brake included, as it iis beyond the ability of most shooters to shoot effectively without one. I was at the range, when a shooter fired a 338-378. Most of the car alarms went off, and kids were crying, and ladies were screaming. Now they have muzzle braked only sessions at the club.
Most of the loads you see published in manuals are considered on the light end and reloaders can safely exceed Speers recommended loads, very carefully!
An associate uses a Vanguard rebarreled to 30-378, and claims kills on elk at over 500yds. With this cartridge I don't consider 500+yards excessive. He hunts with the ear plugs on a cord with one in one ear and puts in the other when he's ready to fire. Many guides will refuse to guide a shooter using a 378 based rifle with a muzzle brake.
They gained some popularity at Williamsport after the Army did their high velocity research with them back in the 50-60's.
They are expensive in every dimension, the brass is outrageous, the rifles are expensive, since only WBY makes them factory, they will test the best optics to their limits, and use 120gr+ powder each.
I'm content to shoot the regular WBY's, they seem almost economical in comparison.