I've been using F.lux for over seven years. Advantages…

- You have a great deal of control over the blue level. Night Shift's blue level is higher than F.lux's default, and not adjustable.

- Flux transitions more naturally as the sun goes down.

- More scheduling options, "disable until tomorrow".

- the big one: disabling per-app or for full-screen apps. You probably don't want Flux on while watching a movie or binging on a videogame. (I set up my lady friend with Night Shift and watched a movie with her recently, spent the whole film wondering why they made such awful color choices)