I'm thinking it'll be a new console, using a new SOC made using AMD's most current power efficient, but cost effective technology available in 2016, like a Puma or Excavator based APU (I would have sad Zen, but I think Zen will be coming to the server market first and supply volumes may not be sufficient for other markets until later), HBM and perhaps DDR4 if memory volume can't be provided all from HBM.
Overall system performance would be at a decent leap over PS4 (it would be a system releasing 3 years after PS4), made to easily run current 3rd Party games, with Nintendo also partnering up with external publishers/developers to get more games to suit that market from the beginning.
Price wise it would be in the same ballpark as PS4 when it releases.
DeNA basically solves the issues Nintendo had with Wii U's online.
The Nintendo spin for this is that it could basically run all software from home consoles to handheld machines, which would give the system a huge library of games to play from day one, plus there would be those new gen titles as well as the core selling factor.
This cross play capability could be handled seamlessly by a secondary SOC or even an MCM similar to Wii U's, only using more up to date tech.
Nintendo could also offer a standard free online system and a premium, subscription model like PS+ and XBL, which gives monthly games, but handled in a unique way to Nintendo.
If NX isn't this, then I think the other possibility is that it's still a Wii U/3DS hybrid, but one that is slightly more powerful.
I don't think the first NX system would be a handheld that can play Wii U games, just because it would be too pricy if it's releasing late next year and battery tech isn't quite capable enough to support a mobile system on that level.