I have a friend who can't train if he's consumed anything other than water in the last 5 hours. I can superset milk with power cleans, and have had to once or twice due to not having the right nutritional balance in my system entering the gym. If I have a typical cereal breakfast, I'll need morning tea and two glasses of milk before I can train properly. If I just have a cup of tea instead of cereal, I can train for 2 hours from just having one glass of milk 15min beforehand. Hormones influence this.
What I'm saying is that there isn't a universally correct answer to your question that applies to every person, or even to the same person. You'll have to figure this stuff out for yourself.
If you're concerned about fat, total energy in vs energy out each day is more important than when you train in relation to your meals. Perhaps if you train while fasted, your body will use more fat for energy. But if you train when not fasted, your body will use up sugars in the system, preventing them from being stored as fat later. If the total energy input and output is the same in both scenarios, then the net result is probably very similar. There's a lot of anecdotes around the place that body composition results vary based on these factors, but I'm not aware of any evidence to back these claims. Of course, absence of evidence =/= evidence of absence....
