The 3DS 2D and 3D are conglomerations of various DQ's.
2D = DQ6esque models, pallete, and tileset, with the battle window shape being like DQ5 and models lacking movement like DQ's 1~5, oh, and the menu layout is more reminiscent of DQ6.
3D = DQ9 with slightly less chibi but still chibi, using DQ10's outlining, only heavier on the black. The camera setting is DQ9's style of 90 degree. The battle system however mixes 8, 9, and 7 3DS. The characters are lined up normally, but the camera is behind the back like in 7 3DS, the menu is more reminiscent of DQ8, and the lineup of enemies is more like DQ's 8 and 9, in a line rather than using rows and columns like DQ7 3DS. At least from what I've seen.
The PS4 version has a more versatile camera that's designed so you can see all of the views from just about anywhere. They deliberately seem to have left the model quality at normal setting at distance, or the degradation is limited, which is cool, so a waterfall doesn't look like junk from afar and great close up...for instance, like in most games.
The PS4 vehicles are built more around exploration, as the PS4 version seems to have a lot more climbing elements than the 3DS, and some vehicles fly or jump...not sure about climbing.
The PS4 maps seem more like 8~10x the size of the 3DS maps, even when comparing the 3DS 3D. It really emphasizes the explorative aspect of the PS4 over the 3DS.
3DS version allows you to see your four members on the field and in towns for both graphical settings, while the PS4 only ever shows the Hero. In the 3DS, if you take the Hero out of the main party, he remains at the fore of the party, and you'll have 5 members showing.
The 3DS has an extra village for the Yochi you see in both games, and a dungeon you recruit Yochi to explore (guessing that's the Labyrinth of Time?). In anycase, the dungeon works like a sidescrolling simplistic Yokai Watch from what I can tell. They find items I guess that allow you to go back to previous DQ's, 1~10. When you go back to the previous worlds, you do so at particular points in their story and work behind the scenes to assure things either happen for that particular hero or that certain things don't happen to that particular hero. That leads to a series of special boss fights, and a series of unique equipment...and at least one extra piece of uber equipment that is present in the PS4 and only appears in a single instance in the PS4 that I'm aware of.
PS4 has more Zoom points than the 3DS, including zooming directly to camping locations (not sure if it's all of them), and to dungeons. I don't know if the 3DS allows dungeon zooming, but I do know the PS4 does, and the zoom list is substantially larger than the 3DS.
PS4 lets you zoom inside buildings, which some believe is an oversight, while others think it's intentional with Western audiences in mind, as Western gamers might be annoyed at having to walk outside to Zoom.
Apparently one of the casino games is much easier to exploit on one of the versions, but I don't recall which game or which system.
When you can fly around, the 3DS allows you to use the shadow to land where you want to based on where you can, while the PS4 has specific landing spots that are shown as rays of glistening light. I think it's one for each area.