I am a big fan of eight millimeters. My goto is my 8mm Rem Mag, a wonderful thumper.
Ballistically, I find the 8x57 & 30-06 to be equals, the 8x68s & .300WM to be equals and the 8mm Rem Mag to fall between the .300Wby and .340 Wby. But if I take into consideration the practicality of factory ammunition and popularity of caliber I would go with the .300WM. It would not be out of place for hunting anything in the western hemisphere nor most of the world. But that’s just me, you may have another preference and you wouldn’t be wrong.
Another candidate would be the .375H&H.