Personally, I �d say they are interchangeable in the rephrased example
 
The movie starts in 5 minutes:
 
1. We are going to be late.
2. We will be late. 
 
 �going to �, in this instance, indicates definite signs/probability that the outcome  �be late � will occur.  
 �Will � is a vey strong word, so as a prediction it indicates a definite rather than an indefinite situation.
 
 In your original example 
The Movie started at 8 o �clock, it �s nearly a quarter to nine now. We _______________ (be) late.  
 
It isn �t a future context, it �s present. We would use something more like  �We are already late. � 
 
Cheers,
AB