APCH CTLR GAVE DSCNT INSTRUCTIONS FOR TFC; TCASII SAID CLB. FLC FOLLOWED CTLR CLRNC; ACFT PASS IN CLOSE PROX.

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ON LOC AT 4000 FT; HEARD 'ACR 3000.' CLRNC CUT-OUT BY TCASII CALLING 'TFC; TFC.' FO CALLED TO CONFIRM CLRNC AND WE WERE DIRECTED TO 'TURN R IMMEDIATELY AND DSND IMMEDIATELY TO 3000.' SEEING PROX OF OTHER ACFT I ROLLED INTO A 50 DEG BANK AND STARTED DSCNT. TCASII THEN CALLED 'CLB XING CLB.' I CONTINUED DSCNT AND TURN. I DO NOT KNOW HOW CLOSE WE CAME TO THE OTHER ACFT. THE VOLUME OF THE 'TFC; TFC' IS TOO LOUD IF IT CUTS OUT ATC. I FEEL THAT IF I HAD LEVELED WINGS TO CLB AS TCASII INSTRUCTED AND OUR OPERATING MANUAL SPECIFIES; WE MAY HAVE WELL HIT THE OTHER ACFT. SUPPLEMENTAL INFO FROM ACN 193480. MLG WAS ESTABLISHED ON LOC AT 4000 FT AND CLRED FOR THE APCH. ATC ISSUED CLRNC 'ACR DSND/ MAINTAIN 3000.' HOWEVER; THE CALL SIGN WAS PARTIALLY COVERED BY THE COCKPIT TCASII ISSUING A LOUD 'TFC; TFC' WARNING. COPLT SET IN 3000 FT IN ALT ARMED WINDOW; BUT ACFT REMAINED AT 4000 FT WHILE THE COPLT CALLED ATC TO VERIFY 3200 FT WAS FOR MLG. AN ATC SUPVR CAME ABRUPTLY ON LINE AND TOLD MLG TO DSND IMMEDIATELY TO 3000 FT IMMEDIATE R TURN TO 270 DEG. CAPT BEGAN EXACTLY THAT; USING 50 DEG R BANK AND PUSHING NOSE DOWN. AT THIS POINT THE TCASII WARNED 'MONITOR VERT SPD' AND THE CAME WAS COVERED IN RED LIGHTS EXCEPT FOR GREEN LIGHTS AT 1500 FPM CLB. CAPT SAYS TCASII ALSO ISSUED 'CLB; CROSSOVER CLB'; BUT I DO NOT RECALL THAT. I FEEL ONCE BEGINNING THE EVASIVE DSNDING R TURN; THE FLC WAS COMMITTED TO THAT COURSE OF ACTION AND AT THAT POINT GOING FROM STEEP DSCNT TO A CLB WOULD HAVE BEEN A HAZARDOUS COURSE OF ACTION. QUESTION: ALTHOUGH YOU MAY DEVIATE (ARE REQUIRED TO BY COMPANY) FROM ATC INSTRUCTIONS DUE TO A TCASII RA; WHO DO YOU FOLLOW WHEN BOTH ARE GIVING DIFFERENT EVASIVE COURSES OF ACTION? AND DO YOU STOP MIDWAY THROUGH ONE COURSE OF ACTION TO FOLLOW ANOTHER?