There is no difference in meaning and the sentences are entirely interchangeable, but which is used can depend on context. The form of verb in these sentences would normally match that of the question which elicited them.
Our world tour starts soon. It's going to take three years.
Ooh. When do you go?
We fly to Paris next week.
When are you going on holiday?
We are flying to Paris next week.
It would be unusual (though unremarkable) to mix the replies and use a form which does not match the question.
If there isn't a question to answer, then the simple present is more perfunctory and formal, and the present continuous more informal and conversational.