Thank you very much. Yes, I think the sentence using an adjective "polite" is correct, too. The problem is I'm not so sure when an adverb is used in this pattern.
a. Tom is the more polite (one) of the two (boys).---correct. b. Tom behaves the more politely (one) of the two (boys).---wrong.
As is obvious, the article before more makes sense when you think that one is