The difference here is one of emphasis. The continuous tense emphasizes the process of the activity... treating it as something that happens over time and emphasizing that time.
The more simple tense (in this case future) merely treats the event as a point in time... or if repeated multiple points in time.
Thus one might say, "I am going to eat dinner at 6 o'clock." In that use the process is de-emphasized, and the time is probably the beginning time.
If one were to say "I am going to be eating dinner at 6 o'clock." then one is emphasizing the process, and the time is probably somewhere in the middle, altho it might be the beginning. (To emphasize the middle one would say '... going to still be eating...".