AN LGT ACR ACFT HAD AN NMAC WITH AN ACR MLG. THE RPTING ACFT SLOWED EARLY AND THE INTRUDER ACFT FLEW UNDERNEATH.

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INCIDENT OCCURRED ON THE KAYUU 1 ARR RTE (KMCI) IN THE VICINITY OF HAIRS INTXN. APCH CTL ADVISED MLG TFC AT 10 O'CLOCK POS CLBING FROM '3500 TO 10000.' SEVERAL MINS LATER; I OBSERVED JET TFC AT THAT POS; LOW; AND CLBING. TFC OBSERVED WAS WBOUND. WHEN QUERIED ABOUT THE TFC A SECOND TIME; I RPTED THE TFC IN SIGHT. SHORTLY AFTER THAT; WE BEGAN A TURN TO A 190 DEG HDG (FROM 120 DEGS) TO FOLLOW THE ARR RTE. AT THE SAME TIME; WE WERE CLRED FROM 11000 FT TO 6000 FT (NOT SURE) REF THE TFC. MY LAST SIGHTING OF THE TFC WAS AT ABOUT THE 8 O'CLOCK POS AND STILL WBOUND. APCH ALSO ADVISED THE MLG CREW OF OUR POS AND WAS ADVISED THAT THEY HAD US IN SIGHT. WE SLOWED TO 210 KTS AND BEGAN OUR DSCNT. EARLY INTO OUR DSCNT; AN MLG PASSED UNDER US. THAT TFC APCHED FROM THE 5:30 POS; AT ABOUT 10000 FT. OUR ALT WAS ABOUT 10500 FT. I HAD EITHER INITIALLY IDENTED THE WRONG TFC OR; THE TFC I SAW TURNED SBOUND AFTER IT PASSED BEHIND ME -- EITHER WAY I SHOULD NOT HAVE BEGUN MY DSCNT. I AM SURPRISED THAT APCH CTL AND THE MLG DID NOT CATCH MY MISTAKE; IT'S HARD TO KEEP TRACK OF AN ACFT AT THE 6 O'CLOCK POS! I BELIEVE THAT COCKPIT WORKLOAD CONTRIBUTED TO MY ERROR. BUSY PHASE OF FLT; WITH CHKLISTS AND PROGRAMMING FOR THE APCH.