The NighSwan, I posted earlier that both sentences are correct, but I deleted my post when others seemed adamant that only the first is correct. But now that you've chimed in, let me expand on your post. After all, I think it's best if the OP gets all information in order to decide which to use.
When the personal pronoun is the subject of a clause, we use the subjective form (she). When the pronoun is the object of a clause, we use the objective form (her).
Many grammarians argue that words such as than are often used as prepositions, so when the pronoun is the object of the preposition, we use the objective form (her). Such usage is now widely regarded as acceptable in all but the most formal writing. And that is why both sentences are correct.
And the inversion test is not infallible. Consider these sentences:
Mary liked John more than I.
Mary liked John more than me.
Now invert them.
I liked John more than Mary. (correct)
Me liked John more than Mary. (incorrect)
But whether or not the original versions are correct, we must know the intent of the sentences. In order to know that, we must parse them.
Mary liked John more than I [liked John]. (correct)
Mary liked John more than [she liked] me. (also correct)*
In the second sentence, the inversion test fails even though the sentence is correct.
*Because of the than=preposition case described earlier, "Mary liked John more than me" would still be correct even if the meaning of the sentence was the same as the first sentence.
