Without context either might be possible. Of course, the most usual use would be: "We're making dinner (as we do every day)." But also: "We're making the dinner (for the wedding reception.)" Let me see if I can fix it so it's "either / or". Well, that was easy. It was already done. So, that both "dinner" or "the dinner" would be accepted. I just added "the dinner" to the hints.
"Δείπνο" is the main meal of the day while "βραδινό" is the evening meal specifically. Depending on where you live and circumstances the main meal could be in the afternoon or evening. For example we could speak of "Το γαμήλιο δείπνο" "The wedding dinner" which would depend on the time of the wedding.