There is a bit of a debate on the subject of "than I" versus "than me." Try to restructure the sentence so that the "I" or "me" becomes the subject: You would say "I am better than," but you wouldn't...
The correct wording is "You are better than I." The way to tell is to finish the sentence - "You are better than I am" is correct, whereas "You are better than me am" would be incorrect.
