The question of which case pronoun to use after "than" is one that has been argued about for over three centuries.
Most common, at least in normal use, is "than them". Athough "than they" was traditionally seen as "more correct" by some (but not all) comentators, nowadays its use is very formal and few people speak like that. It seems we don't really like using subject pronouns without a following verb. On the other hand, "than they do", with its verb is fine.