Do we say He is taller me or He is taller than I?
The difference between the two is that me is an object pronoun and I is a subject pronoun.
While the objective than me may sound more natural to most ears, in formal situations, we use the subjective than I.
The strongest argument for than I comes from ellipsis or grammatical omission. In He is taller than I, the missing verb am can be recovered through ellipsis:
(1) He is taller than I am.
(2) *He is taller than me am.
As pointed out by Quirk et al. (255), in strict ellipsis, when we insert the missing words the sentence should remain grammatical. This requirement is met in sentence (1) but not sentence (2), which is ungrammatical with the insertion of am.
