Use a subject pronoun in a comparison when you’re comparing the person or thing with the subject of a sentence:

Horace is taller than Gordie.

Horace is taller than he.

If a sentence on that pattern seems artificial to you, try adding a verb:

Horace is taller than he is.

In as or than comparisons, using an object pronoun is sometimes correct. Consider this sentence:

Horace likes Eliot more than me.

This sentence mean that Horace likes Eliot more than Horace likes me. If, however, the writer meant that Horace likes Eliot more than he, the writer, does, he would need a subject pronoun:

Horace likes Eliot more than I do.