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 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 long been gaining ground and cannot anymore be considered significantly lesser.