The only difference will be that on the NX, the eshop will be seamlessly integrated into the NX marketplace and UI, which will likely still be the eshop and that, unlike with wiiware, 99% of all retail games released for the Wii U are purchasable on the eshop.
Yes by Wii Mode litrally emulates a Wii and only because the hardware is practiclaly the same. To do a Wii U mode on NX you would need way more power as PowerPC arcitecutre is past it's life, or you have PowerPC bits on the console. If they stick with PowerPC then they will fall further behind the competition.
Also Wii Mode let's me play my physical games. What is the point of a Wii U only mode for digital games? For people like me that is a useless feature as I would need to buy the game again. If they want to capture a new audience, may as well just do what Sony did on PS4 and release some "remasters" of the popular games and you may even get some repurchases too.