Generally the stronger acid will be that molecule which yields a conjugate base that is the weaker base (less strongly alkaline). If you write out the acidic reactions:
CH3OH <---> CH3O[-] + H[+]
H2O <--> HO[-] + H[+]
Now which is the stronger base, hydroxide or methoxide ion? In this case, hydroxide is the stronger base BECAUSE it does not stabilize the negative charge as well as the methoxide ion does. The negative charge on methoxide can be delocalized (distributed among more atoms) and this represents a form of stabilization.
For this reason, CH3OH can stabilize the loss of a proton more easily, and the ability to stabilize the loss of a proton can increase acidity.
