AFTER BEING DELAY VECTORED FOR OPPOSITE DIRECTION LNDG CITATION TFC; FLL CTLR UNABLE TO ISSUE AND UNDERSTAND THE CONTEXT OF B757-200 QUESTIONS OF MISSED APCH INSTRUCTIONS IF ONE OR BOTH ACFT EXECUTE A MISSED APCH.

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FLL WAS UTILIZING RWY 9L FOR ITS PRIMARY ARR RWY. AS WE APCHED ABEAM THE ARPT; AND WERE ASSIGNED A WBOUND VECTOR TAKING US ON AN EXTENDED L DOWNWIND FOR RWY 9L AT FLL; ANOTHER ACFT (A CESSNA CITATION) BEHIND US; APCHING THE ARPT FROM THE E; REQUESTED TO LAND ON THE OPPOSITE END OF RWY 9L; WHICH WAS RWY 27R. WE WERE FINALLY VECTORED ONTO THE FINAL APCH COURSE FOR THE ILS APCH RWY 9L; AFTER AN EXTENDED VECTOR; TO GIVE 'PREFERENCE' TO THE OTHER ACFT SO AS TO ALLOW IT TO LAND OPPOSITE THE ADVERTISED TFC FLOW; ON RWY 27R. PASSING THE OM/FAF; I ASKED THE TWR WHAT OUR MISSED APCH INSTRUCTIONS WOULD BE; NOW THAT WE WERE HEAD-TO-HEAD WITH THE OPPOSITE DIRECTION TFC; LNDG ON THE SAME RWY THAT WE WERE SET UP TO LAND ON! I WAS CONCERNED THAT SHOULD EITHER ACFT HAVE TO GO AROUND; THERE WOULD BE THE POTENTIAL TO HIT EACH OTHER; SHOULD EITHER OF US GO AROUND ON A RWY HDG! THE TWR CTLR APPARENTLY 'MISSED THE POINT;' AND INSTRUCTED US TO FLY THE MISSED APCH 'AS PROMISED;' WHICH WAS 'RWY HDG; AND CLB TO 3000 FT;' AGAIN; IF WE BOTH WENT AROUND; FLYING RWY HDG; THERE WOULD BE A POTENTIAL CONFLICT! AS IT TURNED OUT; OPPOSITE DIRECTION TFC CLRED THE RWY WHEN WE WERE ABOUT 2.5 MI FROM TOUCHDOWN ON RWY 9L. SUMMARY: TO ME; THIS WAS A POTENTIAL CONFLICT SIT; AND SHOULD NOT HAVE HAPPENED. HEAD-TO-HEAD TFC; LNDG THE SAME RWY; HAS THE POTENTIAL TO PRODUCE AN ACCIDENT/INCIDENT.