Quick data dump:
375 Win 220 gr FP launches at about 2,000 fps.
358 Win with 220 gr SP launches at about 2,500 fps.
Sectional density on the 35-caliber bullet is higher.
BC on the 35-caliber bullet is higher.
Muzzle velocity and muzzle energy on the 35-caliber are higher.
Trajectory on the 35-caliber bullet launched 25% faster is considerably flatter.
375 Win is a 150-200 yds cartridge.
358 Win is easily a 350 yds cartridge, but since you asked about elk I would venture a guess at 250-ish yds.
375 Win is a rimmed straight-walled cartridge chambered in older design lever action rifles.
358 Win is a rimless bottlenecked cartridge chambered in more modern lever actions, bolt actions, and single shot rifles.
After running through all this performance data, I wonder why this question was asked.