In some cases, there is very little difference. In others, the 'going to be doing' form focuses clearly on a whole future period and describes the activity that you will be engaged in at that time. For example:
Do you want to come on holiday with us at the end of May?
I can't. I'm going to be studying for my exams then.
This is different from the simple aspect 'I'm going to study for my exams', which is a single 'event' and sounds more like a plan or intention.
One way of understanding the future continuous is to compare it with the past continuous. Look at this:
"I couldn't go on holiday with my friends last May because I was studying for my exams at the time."
In this sentence, we use the past continuous because it's an ongoing activity in progress at a given point in the past. Put this into the future, and you get exactly the same idea of an activity in progress:
"I won't be able to go on holiday with my friends next May because I'm going to be studying for my exams then."
Does that make sense?