Announced at last night's special DQ presentation (which can be seen in it's entirety here:
https://www.youtube.com/watch?v=5Kgmb_k3q5U)
PS4 and 3DS games will have the same story but be different games. The PS4 version will be more like a modern JRPG, similar to DQVIII and is being made using UE4. The 3DS version will be more like a classic DQ and feature both 2D and 3D overworld and battles depending on if you use the d-pad or circle pad. As for the NX version nobody knows what it will be yet but chances are it will be a port of the PS4 version. Both games should be available sometime in late 2016 for the series' 30th anniversary.
Also announced at the presentation were DQX ports for PS4 and NX. A PS4 version might mean it will be localized in the West, but who knows.