The distinction between these two phrases comes down to whether the writer treats than as a preposition or a conjunction. If it is a preposition, the pronoun must be objective—She’s stronger than me; if it is a conjunction, the pronoun must be subjective—She’s stronger than I (the writer here omits a final implied verb: than I am). While than as a conjunction holds greater sway among traditionalists and in formal writing, than as a preposition has slowly been gaining ground and may suit best in certain, more relaxed situations.
When used as a comparative, both subjective and objective pronouns may follow than, though they lead to different meanings: She loves him more than me means that she loves him more than she loves me; She loves him more than I means that she loves him more than I love him.