Z80 instruction set is nicer, but the Z80 was also half the speed per clock cycle, less responsive to interrupts, and more expensive. Hence why the 6502 got slapped in a lot more home computers and the like.
Actually the 6502 designers really intended it more for control systems / embedded.
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.
Actually the 6502 designers really intended it more for control systems / embedded.
The 6809 is the best of the bunch tho.