I always figured the Ready Room was just a location adjoining the Bridge where the Captain could have a private discussion and have some 'down time' but still be immediately available.
The Briefing Room was more for larger discussion with the different department heads, providing information, allowing feedback and the formulation of a course of action.
TMP/Refit should have logically had a Briefing Room on board, but the circumstances in the film moved too quickly for everyone to go to it and have a discussion. The times where it would have been appropriate (Spock's arrival, Genesis proposal tape) they only had three people involved and just held it elsewhere. Using the room in the Recreation Room was a weird choice (and not too private), but the set was cheaper to construct in real world terms.
I would have liked to see what the Refit Briefing Room set might have looked like.