first of all, thank you very much for the information.
In my opinion it should be very clear.
FOLLOW THE TCAS COMMAND. If you see, that a conflict can arise in a couple minutes, because you see it on the screen, than an advice from the ATC is helpful. If the "target" has already reached the TCAS warning area its clear. Follow the commands. The ATC controller is not a good help at this time as he has in the worst case a position indication on his screen which is 6 or 12 seconds old, depending on the radar.
There are only two scenarios which we have to ignor the TCAS command. In the event of a EGPWS call out (hard warning) or a windsheer warning.
Überlingen was a tragic and I hope we never have it again.
The guys on the flights DL 37 / CO 25 on 1987 July 8th had a lucky day, the missed each other by centimeters over the atlantic.
With the new technique (TACS III) and a proper pilot education it should be possible to avoid such scenarios in the future.
Happy flying and trust your avionics (with good airmenship)
