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