if most agree that the 3DS is the one being "replaced" soon, then the first NX iteration will be a handheld, and that obviously wont compete with PS4. Zelda U being postponed until NX for a cross gen release is another popular theory, so that basically tells us how powerful the NX hh will be (around Wii U more or less).
Looking at it in that sense, there won't need to be a "home version" of NX early on, as Wii U will basically be the home version to get some cross gen support. For Ninty they are now full entrenched in HD development, so whatever is being done on WIi U will be moved to NX, and that's a good way to reuse/continue building assets and also a slick way of rebranding. (just like when GCN failed, nintendo basically just upclocked specs for Wii). Nintendo won't push the home console level (NX line) until U gets replaced, and when it does, I don't expect a big jump regardless (xb1-ish levels).
I believe if NX handheld comes out in 2016, the home version will release in 2017 or later.










