The movement data is probably enough to tell when I've slept better or worse, but I wouldn't trust the absolute "number of hours of sleep" they report.
But doctors don't seem to trust the consumer devices (probably with good reason). When I had an actigraphy, they used a special device made by Phillips, and used the results to verify that the sleep study results weren't a one-off night.
My work has been traditionally done with AASM sleep labels which may be a bit more complex that what fitbit uses, so that may bring up their overall accuracy. Additionally I assume that fitbit would use a hidden markov model to predict the sleep stages (which can produce very deceptive results in the context of sleep IMO). I'd say that this would bring their overall accuracy up to around 55% based upon my best guess.