Flux vs Night Shift?
At the end of the day (ho-ho!) it probably just comes down to which effect you prefer, as the science is somewhat inconclusive anyway. Night Shift's effect is more subtle even when turned all the way up, but it's rather less configurable than Flux. 

The article you linked to basically already covers all this, and the relative merits of each:

Flux:


Bigger variety of colour-shifting effects available
More control over start/end time
Can be permanently turned off for specific apps, e.g. video players or photo editors where you don't necessarily want colour-shifting to occur
Can be temporarily turned off for all apps
It's nice to support a 3rd-party developer


Night Shift:


Better system integration; potentially easier on battery as a result (just a guess: I've not measured this, nor heard any anecdotal evidence either way)