NMAC - TCASII; AN ALERT CTLR AND A GOOD SCAN BY THE FLC OF AN ACR AVOIDS A VFR ACFT BY 200 FT.

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DURING DEP FROM JFK ON CLB OUT WITH CLRNC TO 11000 FT THE DEP CTLR ASKED US TO EXPEDITE CLB THROUGH 8000 FT. CO-PLT WAS FLYING. MAX RATE CLB SPD WAS SELECTED AS WAS CLB PWR; SINCE DERATED CLB PWR HAD BEEN SELECTED AFTER CLEANUP AND ACCELERATION TO 250 KTS. DURING THE CLB THE CTLR ADVISED US TWICE OF TFC (IFR) AT 7000 FT AND 4 MI OFF TO OUR R THAT I BELIEVED TO BE THE REASON FOR THE EXPEDITED CLB REQUEST. WE WERE ON AN ASSIGNED HDG OF 220 DEGS. PASSING ABOUT 6800 FT; THE CTLR CALLED TFC; OPPOSITE DIRECTION AT 7500 FT (VFR) THAT HE WAS NOT TALKING TO. THEN ALMOST IMMEDIATELY; HE SAID 'MAINTAIN 7000 FT.' BY THAT TIME OUR ALT WAS 7100 FT RATE OF CLB 1800 FPM. IMMEDIATELY WE GOT A TCASII ALERT; TFC; TFC;' DIRECTLY FOLLOWED BY THE CTLR CANCELING THE 'MAINTAIN 7000 FT; CONTINUE TO CLB.' OUR CLB RATE WAS DOWN TO 1400 FPM AT 7300 FT; AND VERY QUICKLY AFTER 'TFC; TFC;' TCASII FOLLOWED WITH 'MAINTAIN VERT SPD' AND DISPLAYED AN IVSI COMMAND CLB OF ABOUT 2000 FPM WHICH WAS SMOOTHLY FOLLOWED. VISUAL SIGHT WAS OBTAINED AT ABOUT 1 MI BY CO-PLT. I SAW THE ACFT (SINGLE ENG LOW WING) AT ABOUT 1/2 MI; AND WATCHED AS IT PASSED BENEATH US IN A SLIGHT R BANK. IT WAS JUST L OF A DIRECT HEAD ON TRACK. TCASII SHOWED THE RED SQUARE TFC SYMBOL PASSING BENEATH US AT 200 FT AS WE CONTINUED OUR CLB. MY OBSERVATIONS: TCASII IS ACCURATE. FOLLOWING IT'S COMMAND AVERTED A POTENTIAL DISASTER. THE CTLR'S INSTRUCTIONS WERE ALSO CORRECT; BUT BASED ON HIS SCREEN INFO WHICH I BELIEVE GETS TO HIM WITH SOME AMOUNT OF TIME DELAY. I WOULD NOT FAULT THE CTLR. HIS INFO DISPLAY IS THE PROB. TCASII IS A MORE ACCURATE REAL TIME DISPLAY. HOWEVER; HIS WORKLOAD MAY HAVE BEEN A FACTOR IN OUR BEING IN THAT POS; IN THAT THE VFR TFC WAS MENTIONED LATER IN OUR CLB AND NOT UNTIL WE WERE WITHIN ABOUT 500 FT VERT SEPARATION. AFTER MY INITIAL RESERVATION ABOUT TCASII; IT HAS GAINED MY CONFIDENCE.