This is actually the main reason I bought my fitbit. They work great for sleep tracking. The Flex is pretty inexpensive, or if you like the idea of a watch that shows texts and controls music, go with the Blaze.
I used a Fitbit One for about 1.5 years before I bought an Apple Watch. I continued to use the Fitbit for sleep tracking, but was frustrated that it couldn't write to the Health app without the help of a third party. I kept manually entering my sleep hours into Health. Like the Fitbit, Pillow can use the motion sensor on your wrist to detect when you are still vs when you are moving or when you are out of bed. Both Fitbit and Pillow will log time out of bed as "Awake." Fitbit logs movement in bed as restlessness. Pillow doesn't log restlessness. It will use the motion sensor info to determine when to log "Light Sleep" vs "Deep Sleep." Pillow can also record sound to help you figure out how much you snore, and measure your pulse.
The nice thing about using a Fitbit for sleep tracking is that you can wear it while your Apple Watch is charging, but I just charge my watch for a while at night while I'm reading to myself or to my kids. Then I put the watch back on before I go to sleep. Of course if you don't have or want an Apple Watch, then yes the Fibits offer a very good alternative.
Sean