Both tools do the same basic job, which is turning the white of a Mac screen warmer in the evening, so the useful comparison is not a feature list but how each one behaves on your own display in your own room. One evening can give you an initial impression of which appearance you prefer.
Night Shift is built into macOS. Open System Settings, then Displays, then Night Shift. It offers a custom schedule or one that follows sunset where you are, which requires Location Services. Its warmest setting is about 2700K. Nothing needs installing, which is its main advantage.
Sundown is a Mac menu bar app made by Jack Richards. It covers a much wider range, from 6500K down to 500K, keeps a flicker-free display while it dims, and can also follow a schedule so the screen warms at sunset on its own. A longer write-up of the differences is on the Night Shift comparison page.
Use one at a time, because running both makes it hard to tell which one is doing the work. Use the same display, content and room lighting throughout. Temporarily turn off True Tone and automatic brightness, if available, and keep the display brightness setting fixed. Start with Night Shift at its warmest setting about an hour after sunset and read something you know well for ten minutes. Then turn it off, set Sundown to the same rough warmth, and read the same thing. That first pass shows whether the two look alike at similar settings on your display.
For a second pass, keep the same conditions and try a warmer setting in Sundown than Night Shift offers to see whether you prefer its appearance. You may find the Night Shift level is enough, or you may prefer the deeper amber and red end for reading in the dark.
Keep the brightness setting unchanged throughout, while remembering that equal settings do not establish equal measured light output. Note whether the colour of photos and video matters for what you do at night, because the warmest settings change colours a lot. Record each app's settings and your visual impressions. This compares appearance, not measured blue light output.