Thank you for pointing out my mistake in typing.
I'm not 100% sure, but I'm fairly sure that it would be "I" since the sentence could read, "You're smarter than I am." Except with the verb am left out. Of course, I'm recalling 7th grade English Class on this rule. Things could've changed? But in my thinking, since "are" is a linking verb, there is no object. "Me" is the object form of "I" (is it considered objective form; without the quotes, that sentence in itself is wrong). Once again, this could be wrong-just me thought process (intentional). Since writing this initially, I've thought of reasons why my thinking would be wrong... I'm shutting up.
Collikar???
If I'm bored enough to think about any of this stuff... then something is wrong.