A 320 CREW AND KING AIR HAD TCAS RA IN ZNY CLASS E.

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THE EVENTS HAPPENED BACK TO BACK. THE AIRBUS AND ACR X HAVE WEAKNESSES BUILT INTO THE FMC/AUTOFLT (AND I AM STILL RESPONSIBLE). BUT YOU HAVE TO REMAIN ON YOUR TOES TO PREVENT THE SHORT COMINGS OF THE FMC. WAS ON THE ARR TO LGA. CLRED TO CROSS MARCS AT 18000 FT; GOT ATIS AND LGA SHOOTING THE EXPRESSWAY APP 31; I WAS HEAD DOWN BUILDING THE APP (ACR X) DOESN'T PROVIDE ENOUGH MEMORY AND SO WE HAVE TO BUILT TO MANY APPS. IN ANY CASE IF YOU BUILD OR SELECT AN APP AFTER SELECTING A STAR WITH A XING ADDED THE XING SOMETIMES POPS OUT AND ALWAYS (AIRBUS BAD DESIGN). SO THE FO MISSED AS I DID THAT THE XING DROPPED OUT. I NOTICED IT AND SAW WE WERE TO HIGH; ASK CTR FOR RELIEF AND GOT IT; THIS THEN SET A FEW NEW XINGS THAT NEEDED TO BE PROGRAMMED/AND WHILE DIDN'T FEEL TOO RUSHED; MISSED A FREQ CHANGE; AFTER SEVERAL CALLS ( OR JUST ONE MORE) TOOK THE NEW FREQ; BUT NOT BEFORE WE GOT A TCAS RA WHILE LEVEL AT 10000 FT DESCENDING TO 9000 FT. RETURNED TO 10000 FT. KING AIR APPEARED TO BE VFR DOWN TO 10500FT. CTR DIDN'T CALL THE TFC; BUT THEN HE MAY HAVE THOUGHT I WAS ALREADY OVER TO NY APCH. ANYWAY APP SOUNDED LIKE HE WAS WAITING FOR US; AND CLRED US TO DESCEND RIGHT AWAY. SO MUCH FOR A PERFECT FLT INTO LGA.