Franchises where the second film is more broadly acclaimed than the first: Star Wars, The Godfather, The Dark Knight, arguably Alien, Terminator, Star Trek, Paddington, Rocky, James Bond, The Pink Panther, Mad Max. Ones where the third film is the most acclaimed: arguably Indiana Jones, maybe Toy Story, LOTR (kind of all a merged movie so doesn't count), The Good, the Bad and the Ugly, Star Wars prequels