FLC CONFUSION OVER TA GIVEN AND TCASII TA RA ADVISORIES.

Narrative

WE WERE ON 'KEENEBUNK' 3 ARR AT JFK; AFTER PASSING 'ROBER;' DSNDING THROUGH 9000 FT; CLRED TO 5000 FT AND UNDER RADAR CTL. WE HAD A TA; INTRUDER AT 10 O'CLOCK; ABOUT 5 NM ON TCASII DISPLAY--(ACFT X). I WAS UNABLE TO SEE THE TFC BUT THE CTLR GAVE US INFO ABOUT IT. AT THE SAME TIME WE HAD A RA 'CLB XING; CLB'--I DIDN'T COMPLY BECAUSE THE APCH CTLR WAS SAYING THAT TFC (ACFT Z) HAD US IN VISUAL CONTACT AND WAS PASSING BEHIND--ALMOST SIMULTANEOUSLY THE FE; LOOKING DOWN AT THE TCASII DISPLAY CALLED FOR TFC VERY CLOSE; SAME ALT; WHILE A SECOND RA 'CLB; XING; CLB' WAS GOING ON. I PROMPTLY DISENGAGED THE AUTOPLT AND I REDUCED RATE OF DSCNT. I BELIEVE THAT TCASII HAS GENERALLY POSITIVE EFFECTS IN ENHANCING FLT SAFETY BUT SOMETIMES TOO MANY INPUTS CAUSE AN OVERLOAD ON FLC AND COULD BE DIFFICULT TO SELECT THE RIGHT COURSE OF ACTIONS. I WAS INFLT LISTENING TO THE INFO OF ATC; WHILE TCASII ADVISORIES AND FE SHOUTING WERE LIKE BACKGND NOISE BUT ACTUALLY VERY IMPORTANT COMPLEMENTARY INFO I RISKED TO MISS.