It has to run in 1080p. 720p often looks blurry on a 1080p TV.

I often experienced blurryness with X360 and PS3 games running in 720p on a HD TV. And today, a few years later, I would guess my tolerance for blurryness has decreased even more.

1080p really is a perfect resolution. The difference between 720p and 1080ps is huge, but with resolutions higher than 1080p diminishing returns kick in. 1080p is the sweetspot.

60 fps please

I'd rather have higher graphic detail than 1080P. 1080P on NX likely means graphics that are a bit better than Wii U but probably not by much. 

You're on a pixel budget. 

Depends on the game too I guess. A 2D Yoshi game or Mario Maker ... I'd be fine with 1080P, but a Luigi's Mansion game or something ... I'd rather they made the graphical detail as high as possible at 720p. 

The difference between 480p and 720p is huge, but I think 720p to 1080p is less noticable, unless you game sitting right in front of the display. 

Agreed. On Tegra X1, running at 1080p pretty much rules out any major improvement over the graphics Wii U could do at 720p.

One of the saddest questions I heard in a long time.

Technology has changed.
The Xbox 360 and Playstation 3 are not good examples... For one, the Xbox One and Playstation 4 have far better scalers with better filtering.

Secondly, there are technologies such as temporal frame reconstruction which will allow games to output at a higher resolution, we have already had one big success of this technology in Quantum Break, you should go check it out, granted it's still got a way to improve upon.

Whilst there is a difference between 720P and 1080P though, if you have the right approach, the difference can be neglible, granted I am a firm believer of higher resolutions everywhere. (Minimum of 1440P please.)
It's why I am a PC gamer first and foremost.

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The Wii U never had 1080P output for every game.

It will be up to the developers... And just because a resolution is lower, doesn't mean graphics are inferior.

900p minimum. 720p can go screw itself.

The Tegra X1/X2 should be able to run Zelda: Breath of the Wild at 900p-1080p ... but if you're expecting graphical fidelity past that level, that's probably a hard no. 

The chip just isn't powerful enough. 

Honestly, it doesn't really matter to me..

but if I had to pick, I would go with 720

Or 720p with better LoD draw distance, shadows, and a more solid hold on 30fps.