UNNECESSARY AVOIDANCE OF A VISUAL TARGET.

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OUR ACFT ON DSCNT TO 4000 FT; OUR SPD APPROX 190 KTS. LEAVING APPROX 5000 FT. ADVISED BY NEW YORK APCH THAT AN ATR 42 HAD US VISUAL; WAS AT 3500 FT; AND WOULD CLB ABOVE US MAINTAINING VISUAL CONTACT AND SEPARATION. WE ACKNOWLEDGED ATR 42 WOULD BE 12 O'CLOCK TO US (DID NOT SEE ATR 42). WITHIN 1 MIN OR LESS; ATR 42 SHOWN ON TCASII NEARING COUPLE OF MI AND LESS THAN 1000 FT SEPARATION. DIDN'T 'FEEL' RIGHT! SAME TIME SAW GEAR POD MOUNTED LIGHTS AND ACFT AT 12 O'CLOCK LITTLE BELOW ABOUT 1 - 1 1/2 MI. ATR 42 AT ABOUT 10 DEGS BANK INCREASED TO ABOUT 20-25 DEGS BANK. WE STARTED L BANK 10-20 DEGS AS TCASII TURNED YELLOW; 'TA' WITH VOICE 'TFC.' IN FEW SECONDS; TCASII WENT TO 'RA' WITH 'DSND; MONITOR VERT SPD.' WE LEVELED AT 3700 FT JUST AFTER THE ATR 42 PURRED PAST. THE EVENT WAS NOT 'IMMEDIATE' BUT ONE OF THOSE WITH ENOUGH TIME TO REALIZE IT WAS NOT RIGHT AND THE ATR 42 WOULD HAVE VERY POSSIBLY 'NOSE TO NOSED TO US.' ADVISED ATC FREQ 'THAT DIDN'T WORK' FOLLOWED BY MY ADVISING WE WERE '300 FT LOW ON TCASII DEV;' RETURNING TO 4000 FT. NOTHING SAID FURTHER TO INCIDENT BY ATC OR ATR 42. SHORTLY AFTER; GIVEN R TURN VISUAL TO RWY 31; LGA. AS PAX DEPLANED; BOTH FLT ATTENDANTS AND PAX ASKED 'HOW CLOSE THAT LITTLE AIRPLANE WAS?!' WE WERE HONEST; TOLD IT CALMLY LIKE IT WAS AND APOLOGIZED FOR ANY UNCOMFORTABLE FEELINGS. THOUGHTS: 1) NEVER LIKED 'VFR VISUAL SEPARATION IN IFR ENVIRONMENT.' FURTHER REVIEW 'AIM' INDICATES ONLY 1 ACFT MUST SEE OTHER (BAD) BUT MUST BE PAST ACFT CONFLICT. 2) TCASII WORKED BUT CAUSES A REAL 'MIND-ACTION' PULLING WHEN YOU SEE TFC AS WELL AS HAVE TCASII ALERT BLARING AT YOUR EARS AND WANTING TO 'MONITOR VERT SPD' WHEN YOUR TFC IS IN SIGHT 'OUT' -- YOUR IVSI IS 'IN;' AND EVERYONE IS FIXED 'OUT' ON A SILENT 'OH...' MOMENT. 3) PROC STINKS -- IS ANOTHER EXAMPLE OF FAA TRYING TO SQUEEZE MORE INTO UNAVAILABLE AIRSPACE. 4) DON'T BELIEVE ATC ASKED US TO SEE TFC FIRST AND ASKED CREW WHO SAID NOT AS WELL.