Compare these two sentences:
(1) "You love him more than I!" she screamed.
(2) "You love him more than me!" she screamed.
What's the difference? We'll get to that shortly.
You may once have learned that, with comparatives, you're supposed to use the nominative (subjective) case rather than the accusative (objective, direct-object) case because what comes after the comparative than is supposed to be a clause. In other words, you're supposed to write "I," not "me," because the full sentence would read, "You love him more than I do!"
The problem is that this is wrong: there's no reason to assume that what follows the comparative than will be a clause. You may be erroneously assuming that the than is a subordinating conjunction introducing a dependent clause—which it definitely is if a clause comes after it. But the than can also be a preposition, in which case what follows it should be the object of a preposition. (For a more detailed explanation, see the usage notes for this Dictionary.com entry on the word than.)
So the above two sentences are both legitimate, but they mean different things. As we asked earlier: what's the difference? It's this:
Sentence (1) is saying, "You love him more than I love him!"
Sentence (2) is saying, "You love him more than you love me!"
Alles klar, ich hoffe?