The world is larger and more well interconnected, the characters are far more interesting/different, the gameplay is basically the same but with slightly better monster designs in some cases. The chapter system is far superior to anything in the previous games.

I have never played any of the remakes so I can't speak to how those have improved or worsened any of these games, but the original DQIV is much better than the original DQ I-III (even though I love all Dragon Quests).