B737-300 CREW RECEIVED TA AND TCASII TA ON FINAL APCH.

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THE WX IN ABQ WAS 2 MI OVCST; 1/2 MI SNOW; MIST; FOG. WE WERE FLYING THE ILS; RWY 3 AND WERE ADVISED THAT THERE WAS TFC OFF TO OUR R AT APPROX 2 MI. WE WERE CLRED TO LAND. WE RECEIVED A TCASII TA FROM THE TFC (TCASII ALERTED ONCE) AND LANDED WITHOUT INCIDENT; BREAKING OUT AT MINIMUMS. ONCE CLR OF THE RWY; GND GAVE ME THE PHONE NUMBER FOR THE TWR AND ASKED ME TO CALL. WHEN I CALLED; THE TWR SUPVR ASKED IF I HAD HEARD THE CTLR TELL ME TO ABANDON THE APCH AND TURN L. I DID NOT HEAR ANY INSTRUCTIONS TO ABANDON THE APCH AND SO INFORMED THE SUPVR. SHE SAID THAT SHE ASSUMED THAT WE DID NOT HEAR THE INSTRUCTIONS; SINCE WE DID NOT ACKNOWLEDGE AND DID NOT COMPLY. SHE SAID THERE HAD BEEN A SMALL ACFT ON APCH IN FRONT OF US WHO HAD MISSED THE APCH AND TURNED TOO FAR TO THE S ON MISSED APCH; CAUSING A CONFLICT WITH MY ACFT. SHE ALSO SAID THAT THE TWR HAD COMMITTED AN 'OPERROR.' WHEN I GOT BACK TO MY ACFT; I ASKED MY FO IF HE HAD HEARD THE ABANDON APCH INSTRUCTIONS; AND HE SAID NO. AFTER THE NEXT LEG; WHEN I ARRIVED IN PHX; AN AGENT INFORMED ME THAT I NEEDED TO CALL THE TWR IN ABQ. I SPOKE WITH ANOTHER TWR SUPVR WHO INFORMED ME THAT THERE WAS NOT AN 'OPERROR' AFTER ALL. THEY HAD REVIEWED THE TAPE AND SAID THAT THE CTLR MAY NOT HAVE PUT OUR CALL SIGN AT THE BEGINNING OF HIS XMISSION TO ABANDON; AND THAT HIS INSTRUCTIONS WERE RATHER RAMBLING SO THAT BY THE TIME HE HAD COMPLETED THE INSTRUCTIONS; THE OTHER ACFT WAS PAST AND ABOVE US.