Further to Woks reply. Agree with the strong case for TA only mode.
The other thing to bear in mind is if you are doing an emergency descent, almost by definition you are fairly high, so there is a good chance that at least one of the aircraft is subject to climb inhibitions.
Got to go to work, so not a detailed response, but if you think about it, if the other guy can't climb, you are almost certain to get told to level off - ("Adjust Vertical Speed"), i.e. told to stop your emergency descent.
CPB