I have run both fuels in my Ron's Flying Toilet mechanical injection system.

I like them both. I run E-85 ethanol mainly because it is the cheapest when you include the amount of fuel used.

Methanol will be slightly quicker and run a little cooler.
Ethanol is less corrosive (when both absorb moisture),
Ethanol is less likely to contaminate the oil,
Ethanol warms up the engine quicker, which uses less fuel.

Both need a carb/system setup specifically for that fuel.
Since the flow rate needed for methanol is higher, you need a higher flowing fuel system.

My wide band oxygen sensor (Innovate LM-1) works fine with both fuels.