Which will happen first and why?
I think NS TV would make a lot of sense actually. PS TV is a lot cheaper than Vita and the same could happen here, and there would be no whitelist or compatibility issues, would be a full fledged console, cheap, and just as good for some. Actually it could happen at launch or not long after.
NS Mini maybe 3-5 years later? I don't know. And probably a New/Pro/Scorpio version.