I agree with most of the comments here, there basically isn't a good option right now to do this. Natively, the Health app can direct some data to the Fitbit. To add on top of that, the Apple watch definitely doesn't track as much detail as the Fitbit does. There are no native sleep apps on the Apple Watch, though there are 3rd party apps. So I think if you are really set on fitness tracking, then Fitbit is still the best option right now.
A better question to ask is, how much quantification do you really want? Fitbit gives you the most data and breaks it down for you. Apple Watch can track a variety of exercises and the Health app can break that down to a certain extent. I find that the Apple watch is fine for what I need it for, which is that the smart watch functions out weigh the fitness tracking abilities.