Been in the TU Sim several times (other sim however) and talked to a lot of TU crews. All of them concurred that if a TCAS goes off they are not going to heed ATC commands but to follow TCAS no matter what. One put it brutally by saying "Why should I listen to the one who put me into a situation for the TCAS to go off in the first place?" While I find this a tad one sided, as a TCAS alert can be triggered by pilots mistakes as much as ATC mistakes, the gist of it is, when a TCAS goes off I'll follow it first and ask questions later.
Obviously the worst case scenario is if one guy follows TCAS and the other doesn't. So, if you get a TCAS RA and can't rely on the other guy to act on it, then things will go pearshaped very quickly.
I reckon that the Ueberlingen accident has brought that message home to just about all the TCAS users who care to read up on it. So let's hope that this will never ever happen again.