You can write Zilog 80 programs and games (as I do) on the Commodore 128. I exploit Z88DK, which does the magic of booting the C128 in Zilog 80 mode.
The Zilog80 at 2mhz effective speed is about as fast as a MOS6502/8502@1mhz in many situations.
In some situations that depend on a bigger hardware stack, the slow Zilog80@2mhz can beat the MOS6502/8502@1mhz.
This is the case when you write your games in C with CC65/Z88DK dev-kits.
My games are written in C + my abstraction layer CrossLib so that I can compile C128 versions in both MOS8502 and Zilog80 mode. I use equally good compilers for MOS8502 and Zilog80 (i.e., CC65 for MOS6502, SCCZ80 for Z80 and Intel8080 as part of Z88DK, as well as a dozen other cross-compilers). I know that this is not a scientific proof but both compilers have been developed and optimized over many years and both come from Small-C.
You can take a look at my project and even test the binaries of my games (also in exotic C128 modes as such Zilog 80 non-CP/M):
Source and doc: https://github.com/Fabrizio-Caruso/CROSS-CHASE