Frogger on 18 June 2015
No they shouldn't. That would be stupid.
What Nintendo and Sony should do, something that would be incredibly intelligent and forward thinking, is allow for cross-platform online play between the PS4 and the NX. Any multiplat with online multiplayer is playable with each other, whether you're on PSN or the NN. Android and iOS already do this.
Having these guys do it as well would be far more beneficial to both companies.
