So, to answer the question of "What's new in the remakes of DQIV?":
- First, it added a new option for control of your party in Chapter 5: manual control. Yes, you no longer have to rely on the judgement of a questionable AI in the thick of combat. That said, there is a good reason to do so anyways - the AI chooses the action of the party member when their turn in the round arrives, rather than at the start of the round. This means that unlike you, the AI can actually react if things should go pear shaped during the current round of combat.
- Second, it adds a bonus chapter. In this chapter, it becomes possible to save Rosa, prevent Psaro from transforming, and then buddy up with the reformed boss to go hunt down Amon (the guy behind Rosa's death originally) and give him the ass-kicking he so richly deserves. Of course, to do this, you have to trek through a very long, very difficult bonus dungeon, culminating in a gag boss team that will make you wonder which dies first - the chicken or the egg? And you'll have to repeat this fight several times to fully kit out Psaro.
- Third, the US version (released on the Nintendo DS) received a new translation that gives several of the characters specific accents, like Ragnar's Scottish brogue, or Alena sounding like the villain from a bad 80s movie. It's a much better translation than the NES original. Sadly, we did lose one feature from the Japanese version - the ability to talk to your current party members, which could result in some rather hilarious commentary.