In You treat her worse than I treat her, t. is a strong or subordinating conjunction, attaching an adverbial clause to its owner worse. In You treat her worse than I, the same account may be given with the explanation that there is an ellipsis of treat her; or t. may be called a weak or coordinating conjunction linking the two similarly constructed nouns you & I. In You treat her worse than me, the same two names for t. are possible, but the ellipsis is of you treat (not treat her), or the similarly constructed nouns her & me (not you & me); those are the possibilities if the sentence is said with the only sense that an educated person gives it. But an uneducated person may mean by it You treat her worse than I treat her; &, if it is to be so taken, t. is not a conjunction of either kind, but a preposition governing me. Doubts whether a word is a presposition or a conjunction or both are not unknown...It is obvious, however, that recognition of t. as a preposition makes some sentences ambiguous that could otherwise have only one meaning, & is to that extent undesirable.
Boldface added by me.