I think there's more debate on this than fact. Exercising in a fasted state might burn more fat, but it just might burn muscle too.
I work out at night, both lifting and cardio (different nights), and I can't say it has helped my sleep any. In fact, there are a lot of nights I can't fall asleep because I am too energized from the workout.
If I had the pleasure to do what I wanted, I'd do cardio in the morning, but I'd eat a banana and a protein shake about a half hour or so beforehand.