I would make sure the drivers are installed (you’re using an up-to-date VMWare Tools etc) and switch. You can leave the MAC address the same and simply swap out the controller type which Windows doesn’t seem to care too much about.
As said previously, the E1000 is emulated, it is not physically present, so it isn’t “better” in any sense of the word, latency would be a byproduct of the emulation. It is there for systems that you want to virtualize but for whatever reason can’t or doesn’t yet have the VMWare drivers installed (eg. Windows 95, DOS, VMS or during installation of Windows…)