So far from what we've seen:
- The PS4 version is a full open-ish world 3D game with jumping, platforming, exploration, and is fully proportional in scale like DQVIII. They didn't show any battles, but enemies are visible on the field, and it seems really early.
- The 3DS version has 3D graphics on the top screen and 2D graphics on the bottom screen. Looks to be reusing a lot of existing assets, but looks great regardless. There's two versions of everything for 3D/2D - towns, fields, battles, event scenes, etc. If the player uses the analog slidepad, 3D battles will initiate and the battles on the field will be symbol encounters (you see the enemies and can avoid them), if you use the d-pad, battles will be in 2D and they will be random encounters.
- Currently the 3DS version looks way more complete than the PS4 one. But both are slated to be released within the Anniversary next year in 2016.