NMAC BTWN A DEP IFR DHC8-200 ON A RADAR VECTORED HDG AND AN ARRIVING VFR GA ACFT DSNDING INTO THE TFC PATTERN FOR RWY 4 AT EWN; NC.

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WE WERE CLRED FOR TKOF BY NEW BERN TWR (EWN) OFF RWY 4. I WAS THE CAPT AND PF. WE WERE SWITCHED TO CHERRY POINT APCH; ON CLBOUT; BEFORE WE HAD CLBED THROUGH 1000-1500 FT. WE CHKED ON WITH CHERRY POINT APCH AND WERE CLRED TO; I BELIEVE; 3000 FT AND WERE ASSIGNED A 320 DEG HDG FOR 'SEQUENCING' WITH; I ASSUMED; OTHER IFR TFC. PASSING THROUGH APPROX 1500 FT; WE WERE ISSUED A TFC ALERT BY APCH FOR TFC THAT WAS AT OUR 1 O'CLOCK POS; SEBOUND; ABOVE OUR ALT AND DSNDING. THIS TFC ALSO SHOWED ON OUR TCASII. APCH WAS NOT WORKING THIS TFC. ONCE WE WERE ESTABLISHED ON THE ASSIGNED 320 DEG HDG; WE RECEIVED ANOTHER TA FROM APCH AND HE ASKED US IF WE WERE VMC. WE WERE. WE DID NOT HAVE TFC IN SIGHT. THE TCASII SHOWED THIS TFC NOW COMING DIRECTLY AT US; ABOVE US; DSNDING. I LOWERED THE NOSE TO HAVE A CHANCE TO SEE THIS TFC; AND I DECIDED TO START A TURN TO THE W THE TFC WAS RPTED FLYING SE AND WE WERE FLYING NW ON AN OPPOSITE COURSE. I BELIEVED A WESTERLY TURN WOULD HELP KEEP SEPARATION WITH HIM; HAVING HIM PASS OFF THE R. HE STILL SHOWED A 1 O'CLOCK POS ON TCASII; INSIDE THE 2.5 MI SCALE. APCH GAVE; I BELIEVE; ANOTHER ADVISORY AND SAID THAT OUR TARGETS WOULD MERGE. I KEPT TURNING FARTHER TO THE W; THEN SW TO GET ON A DIVERGENT COURSE. THE TCASII THEN LIT UP RED; SHOWED THE TARGET AS A COLLISION THREAT; AND GAVE US AN RA TO CLB. I WAS THEN FIXATED ON THE TCASII TO TRY TO FIGURE OUT HOW TO MISS THIS ACFT; AND FIGURE OUT EXACTLY WHAT HE WAS DOING. I COMPLIED WITH THE RA WHICH WAS COMMANDING A CLB. I BROUGHT THE ACFT UP TO 20 DEGS NOSE-UP PITCH AND WE HAD MAX CLB PWR. WE RAPIDLY CLBED THROUGH 2000 FT FOR 3000 FT. LAST TCASII PLOT I SAW WAS THE OTHER ACFT TARGET SITTING ON TOP OF OUR ACFT SYMBOL WITH A -100 FT FOR RELATIVE ALT. I BELIEVE WHAT HAPPENED WAS; THE ACFT WAS DSNDING FOR LNDG INTO EWN. HIS POS AND COURSE PUT HIM INBOUND TO DOWNWIND. WHEN WE WERE ASSIGNED A 320 DEG HDG; WE WERE LESS THAN 1 MI OFF THE RWY. WHEN THE TFC WAS ORIGINALLY CALLED OUT BY APCH; HE WAS INBOUND. AS I STARTED TO RUN TO AVOID HIM; HE WAS TURNING TO THE SW TO ENTER THE DOWNWIND. I HAVE TO ASSUME THAT IS WHAT HAPPENED. IF HE HAD BEEN AN OVERFLT AND MAINTAINED THE SE HDG; ONLY MANEUVERING WOULD HAVE GIVEN US GOOD HORIZ SEPARATION. A VERY BIG PROB THAT I HAVE WITH THIS SIT; THAT I FIND INEXCUSABLE; IS THAT 2 ACFT; IN CTLED AIRSPACE (EWN ATA); TALKING TO AN ATC FACILITY; COULD COME SO CLOSE TO HAVING A MIDAIR COLLISION. THE PROB IS THAT EVEN THOUGH WE WERE WELL INSIDE THE EWN CLASS D AIRSPACE; WE WERE BEING WORKED BY 2 DIFFERENT ATC FACILITIES. HE WAS ON EWN TWR FREQ. I WAS ON CHERRY POINT APCH. HOW COULD THIS SIT BE AVERTED? NEW BERN TWR COULD HAVE TOLD US OF THE INBOUND ACFT; HAD US CLB RWY HDG TO 2000 FT; AND NOT SWITCHED US OFF HIS FREQ UNTIL WE WERE WELL NE OF THE ARPT AND TFC PATTERN. HE OWNS TO 5 NM AND UP TO 2500 FT AGL. OR; CHERRY POINT APCH COULD HAVE HAD US CONTINUE RWY HDG TO 3000 FT UNTIL WE WERE N OF THE TFC; OR ABOVE HIM. A CLB TO 3000 FT TAKES ABOUT 90 SECONDS IN A DHC8-200. EVEN THOUGH WE WOULD BE HDG OPPOSITE DIRECTION TO OUR FLT PLAN RTE; 90 SECONDS IS NOT THAT MUCH OF A DELAY. I REALIZE THAT CHERRY POINT APCH HAS NO LEGAL RESPONSIBILITY TO SEPARATE US (AN IFR ACFT) WITH A NON PARTICIPATING VFR ACFT; HOWEVER; 'TECHNICALLY CORRECT TO THE POINT OF IMPACT' IS NOT ACCEPTABLE. AGAIN; 2 ACFT IN THE SAME AIRSPACE; ON 2 DIFFERENT FREQS; WITH 2 DIFFERENT ATC FACILITIES WAS A MAJOR CONTRIBUTOR TO THIS SIT.