In some books it is written that +M (mesomeric effect) effect of OH is less than that of OR . The reason they give is inductive effect of R (group) which sounds senseful . But at some places it is written +M of OR is less (which is correct). But I am not able to understand the reason which they give.
First of all, you must understand that the reactivity of OR changes as you change the alkyl group (-R).
For example, consider, the methoxy group (-OCH3), as per proton NMR spectra of anisole and phenol, the reactivity is almost similar in both the cases. In fact the reactivity is so similar that undergraduate texts just mention the fact that anisole has reactivity similar to phenol. (Source 1)
On the other hand, if you consider more bulky alkyl groups, steric hindrance might be a contributing factor to reactivity, competing with the mesomeric effect. But to a large extent, it is sufficient to say that both hydroxyl and (-OR) groups have similar reactivity.