The answer is <em>B: You are much more logical than I.</em>
In formal English we keep I/we, when making comparisons, because the pronoun is still considered to be the subject of the verb, even though when the verb has been ommited: "I am not as old as you (<em>are</em>)". However, the use of <em>me/us</em> is more usual in <em>informal English</em>, as in A: <em>than him</em>; in C: <em>as them</em>; in D: <em>than her.</em>
Actually, the correct sentence is the following one "You are much more logical than I". Think about it as if it was a short version of the sentence
"You are much more logical than I am".: here you couldn't say "You are much more logical than me am". that's why you also should not say it in the shorter version.