Water and methanol injection does the same job in different ways, they both perform in-cylinder cooling and knock suppression well.
Water has a higher latent heat value than methanol, you need to inject twice the amount of methanol by mass to extract the same amount of heat during combustion. This is why all pure alcohol injection systems require a bigger jet. By volume, you need to inject 2.5 times more than water.
Effect on knock suppression is totally different. Water suppresses knock by quenching peak flame front temperatures hence regulating the frame propagation speed – (too fast burn promotes knock). In-perfect charge distribution produces lean and rich pockets. Lean pockets burn at a higher temperature (oxygen-rich = faster) compared to fuel-rich pockets (excess CO slows down burn speed).
Alcohol suppresses detonation by increasing the knock threshold value of a given fuel grade. Since large amount of alcohol is required to control in-cylinder temperatures, air/fuel ratio will be affected significantly. Some fuel has to be removed to avoid over-rich mixture.
As far as power production capabilities is concerned, both methods will yield good power increase, but is done very differently:
Methanol increases octane to allow high boost whereas water can allow very high boost at very lean conditions, power is being produced by increasing the effective compression ratio without the penalty of high EGT. Alcohol power increase is purely based on raising the octane value and cooler EGT.
Water alone has a higher potential of extracting more power in extremely applications such as the WRC cars where CR ratio of 10:1 at pressure ratio of 4. Some reference below:
In Diesel application, the extreme use of “effective compression ratio” is being employed in this example below where power is being limited by excessive EGT. Water/steam allows the serial turbo configuration running in excess 80psi absolute, extracting a targeted 750 BHP at 710degC EGT instead of 550BHP at 750deg C EGT. Abstract below:
I hope you are able to identify the merit of both systems and use it according to your needs.