Its fairly clear cut.
The plan of PS4/3DS tells you exactly the state of the industry in Japan, the PS4 (if anything) is there for the west. They're not crazy enough to let their franchise rot on PS4 in Japan but, all the same, the 3DS version is going to eat heavily into the PS4 sales same as 3DS Smash ate into Smash WiiU... which ends up becoming a bit of a self defeating prophecy in "saving consoles" but theres only so much money you'd burn on a hopeless struggle. The only difference between the two games is graphics from what has been shown (and possibly some of the overall world design) with the 3DS, of all things, seemingly having more features and nostalgia hooks. I would expect sales to be heavily lopsided, and the story being the same is going to greatly limit double-dipping outside of the core players, who probably already own all the relevant consoles.
The reason the NX showed up is because SE is also hedging their bets on building up a new fanbase on the next handheld because even if it will probably sell less than the 3DS, it will still likely dominate the market.
The market is currently volatile and heading towards a big inflection point when the 3DS retires. Either consoles magically recover (they won't, and the PS3's ability to sell software is anemic and the Vita is a path already laid low), or publishers who want to sell games in Japan needs to hope that the next handheld does well and replaces the 3DS. If nothing steps up, without the 3DS, the market losses half of its entire software moving capabilities. Obviously, though, Nintendo would not want that to happen and is likely making deals with various developers in Japan. This is probably one such deal and, more than likely, means that SE has their hands on development blueprints or kits for the NX.