The acidity of a compound is determined by the stability of its conjugate base. The more stable the conjugate base, the more acidic the compound. The conjugate base of an alcohol is an alkoxide ion, which is a negatively charged oxygen atom. The oxygen atom in an alkoxide ion is more electronegative than the nitrogen atom in an ammonia molecule. This means that the oxygen atom in an alkoxide ion can hold the negative charge more tightly than the nitrogen atom in an ammonia molecule. The more tightly the negative charge is held, the more stable the conjugate base and the more acidic the compound.
Therefore, alcohols are less acidic than ammonia because the conjugate base of an alcohol is less stable than the conjugate base of ammonia.