I dont work for a freight airline but do operate night mail on an ATR from time to time. For us, there is no variation. We fly a triangular route leaving our home base at about 8:30pm and arrive back at 6:30am with three and a half hours off between 1am and 4:30am.
The main problem I have with it is tiredness. There is just enough time in the break to fall alseep which is a real killer. I tend to sleep 2 hours in the break and then try to sleep another 4 during the day. After 3 nights of this it really does catch up on you! I once did three night of this followed by two late shifts with only 17 hours off between shifts. That doesnt give you time to catch up or adjust the sleeping pattern.
You also tend to spend a lot of time waiting around and do fairly little flying. We are away for 11 hours but only get 3 in the log book.
The plus side is that you can usually relax a little and dont have to worry about passengers not turning up and airports tend to be less busy at night which means less time at the holding points and less delays enroute.
Hope this gives you some useful info. This is just my personal experience.
Any questions please ask.