Although Z80 has lower IPC, it had a roughly 2x clock speed so performance was about the same Z80 slightly faster for most applications.
It would be rare however for there to be a direct "bake off" between the two CPUs -- any given design organization was either an 8080/Z80 shop or a 6800/6502/6809 shop. There weren't sufficiently great differences in price/performance between the two to make it worthwhile changing.
You could get a BBC Model B (6502 2MHz), add the 3MHz 6502 board, add the 6MHz Z80B board, and do a "bake off" between all three (obvs. scaling for clock speed.)
Then add the 8MHz ARM1 board and watch it smoke the rest into dust, I suppose.
It would be rare however for there to be a direct "bake off" between the two CPUs -- any given design organization was either an 8080/Z80 shop or a 6800/6502/6809 shop. There weren't sufficiently great differences in price/performance between the two to make it worthwhile changing.