Not sure which (if any) apps will deliver insight into the data that it's collecting about your sleep, but perhaps you can do some analysis of your data yourself.
Here's what I mean. Take a look at the outlier data. Focus on the mornings that you either wake up really tired, or really refreshed. Keep track of things that you did the day/night before these outliers. You might find some patterns.
For instance ...
When you wake up tired, it's usually because you went to bed too late. Then you realize that most of the nights when you went to bed too late, you had worked out after 6PM. So maybe make a change to workout in the mornings.
Or perhaps on the mornings you wake up refreshed, you typically went to bed before 10PM. And on those days, you didn't drink any coffee after lunch. Then you would try to not drink coffee after lunch.
The flaw in this is that you have to keep track of more stuff. That's where an integrated system that tracks all of this stuff, combined with machine learning, can deliver insight into how your body reacts to the world around it. Unfortunately, there's not really an app for that. Maybe fitbit has something in its ecosystem. They already track workout, sleep and food intake. If Apple were to take this data and combine it with what they know about you (work schedule, commute, stress) then we'd have the holy grail. But don't hold your breath.
