Than is both a subordinating conjunction, as in She is wiser than I am, and a preposition, as in She is wiser than me. As subject of the clause introduced by the conjunction than, the pronoun must be nominative, and as object of the preposition than, the following pronoun must be in the objective case. Since the following verb am is often dropped or “understood,” we regularly hear than I and than me. Some commentators believe that the conjunction is currently more frequent than the preposition, but both are unquestionably Standard.
And here is actual practice in American English books, courtesy of Google Ngrams — the red line represents “older than I” and the blue line “older than me.” (I compare “older than I” with “older than me” because it seems to me less likely to yield false positives than a “better than” comparison would yield. Even to the commenter to whom I’m responding, “she likes him better than me” would be acceptable, because he would view it as “she likes him better than [she likes] me.” I don’t think this confounding factor would arise much with “older than.”) “Older than I” used to be materially more common than “older than me,” but “older than me” always enjoyed some frequency, and nowadays is just slightly less common than “older than I.” [UPDATE: I originally included the wrong graph, which showed very different results; sorry about that.]
Now of course if by “acceptable,” you mean “acceptable to me” or “acceptable to self-appointed guardians of what they see as proper English,” it might not be acceptable. But if you ask about actual usage, including the actual usage of some of the most respected writers in the English language, “he is a much better advocate than me” is indeed acceptable.
UPDATE: Commenter bernard11 noted that I misanalyzed the meaning of my examples (the Shakespeare one), which made it inapt; I’ve replaced it with a sound example. Thanks for the catch! I’ve also corrected the Dickens example.