The English grammar question is an old chestnut. Here's one place where it is discussed: http://grammar.quickanddirtytips.com/than-I-versus-than-me.aspx For indirect and direct objects in Italian, use "mi". For objects of prepositions use "me." Lui mi oda. Mi legge il libro. Leggi piu' libri di me.
Very interesting read. I particularly like how they discuss how "She reads more books than me" could sort of mean "She reads books more than she reads me" which doesn't make a whole lot of sense.
Though I do have to say that "She reads more books than me" sounds a bit more natural in modern American English than "She reads more books than I". In my opinion, you need to write "...than I do" to make it sound right.