B757 FLT CREW HAS TCASII RA DURING APCH TO SJC.

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ON FINAL APCH TO SJC; WE WERE BELOW 4000 FT INSIDE OF KLIDE IN VFR CONDITIONS. WE WERE TALKING TO SIERRA APCH. WE CALLED THE RWY IN SIGHT AND WERE CLRED FOR A VISUAL APCH TO RWY 30L. IN THE SAME TIME FRAME SOMEWHERE BEHIND US; AN RJ WAS CLRED FOR A VISUAL APCH TO RWY 30R. SIERRA APCH SAID HE HAD US IN SIGHT AND WAS BEHIND US AT OUR 4-5 O'CLOCK POS. WE WERE UNABLE TO SEE HIM. WE WERE ON GS AND LOC FOR RWY 30L AT 200 KTS SLOWING TO 180 KTS. APCH TOLD US TO CHANGE TO TWR. AT THAT TIME WE RECEIVED AN RA CALLING FOR IMMEDIATE MAX CLB. I INITIATED THE CLB. TCASII SHOWED A TARGET 400 FT BELOW AND JUST BARELY BEHIND US ON THE 5 MI RANGE. WE RPTED THE RA AND THAT WE WERE CLBING IN RESPONSE TO THE RA. APCH SAID THE TARGET WAS THE RJ AND THAT HE HAD US IN SIGHT AND WAS 3-4 O'CLOCK AND 1/2 MI ON A VISUAL TO RWY 30R. I TERMINATED THE RA CLB. (IN RETROSPECT; I PROBABLY SHOULD HAVE CONTINUED TO FOLLOW THE RA AND NOT HAVE TRUSTED APCH CTL'S WORDS THAT IT WAS OK.) MY FO WAS FINALLY ABLE TO SEE THE RJ. HE WAS 4-5 O'CLOCK POS GOING TO 3 O'CLOCK POS AND OVERTAKING US; NOW LESS THAN 200 FT FROM US AND SLIGHTLY LOW. WE WERE STILL ON THE RWY 30L LOC AND NOW VERY HIGH DUE TO THE RA CLB. THE RA WAS STILL SOUNDING. THE RJ MOVED ABEAM US (COCKPIT-TO-COCKPIT). HE WAS NOW AT THE SAME ALT AND LESS THAN 200 FT FROM US. I MOVED L; PULLED OUT THE SPD BRAKES TO DSND AND TURN AWAY FROM HIM WHILE KEEPING HIM IN SIGHT. I WANTED SAFE SEPARATION FROM HIM. TCASII WAS NOW COMMANDING AN RA MAX DSCNT. AS I DSNDED AWAY FROM HIM AND WAS MOVING L; THE RJ APPEARED TO BEGIN MOVING R AND MOVING BACK ABEAM TO SLIGHTLY AFT OF US. HE WAS STILL VERY CLOSE; BUT I NOW HAD ALT SEPARATION FROM HIM. I WAS NOW LOW AND HAD HIM IN SIGHT UP HIGH; BUT STILL ABEAM US. WHEN I WAS SURE OF CLRNC FROM HIM BECAUSE OF MY ALT SEPARATION; I MOVED BACK R TO THE RWY 30L LOC AND LANDED SAFELY ON RWY 30L. THE RJ LANDED ON RWY 30R AT THE SAME TIME. IT WAS A WING LNDG; ONLY ON DIFFERENT RWYS. RWY 30L&R ARE APPROX 500 FT APART. I TALKED TO THE CAPT OF THE RJ AFTER LNDG. HE VERIFIED WHAT HAD OCCURRED AND APOLOGIZED PROFUSELY FOR BEING SO CLOSE TO US. IT WAS A MISTAKE ON HIS PART AND HE ACKNOWLEDGED THAT. I ALSO TALKED TO THE SJC TWR AND TO SIERRA APCH. BOTH INDICATED THAT AS RWY 30R IS A NEW RWY; THERE ARE NO PROCS IN EFFECT REGARDING PARALLEL LNDGS TO BOTH RWYS AT THE SAME TIME. THIS WAS A POTENTIALLY DANGEROUS EVENT -- EVEN IN VFR CONDITIONS. I DID NOT KNOW WHAT THE RJ WAS DOING. IT SCARED BOTH MY FLT ATTENDANT AND MY PAX. THE PAX WERE TELLING US THE COLOR OF CLOTHING WORN BY THE PAX IN THE RJ. I DON'T KNOW IF THIS WAS AN EXAGGERATION ON THEIR PART; BUT HE WAS VERY CLOSE TO US. IT MAY BE REFLECTIVE THAT SOME OF THESE PAX WERE REALLY SCARED BY THIS EVENT. FROM COMMENTS HEARD BY THE FLT ATTENDANT FROM PAX WHILE DEPLANING; THE COMPANY MAY YET HEAR FROM SOME OF THEM. IN SUMMARY; ANOTHER ACFT THAT HAD US IN SIGHT OVERTOOK US FROM BELOW AND WE ENDED UP WITH MINIMAL SEPARATION. I'M NOT SURE WHAT THAT SEPARATION WOULD HAVE BEEN IF I HADN'T CLBED IN RESPONSE TO THE RA AS IT SHOWED 400 FT THE FIRST TIME I WAS REALLY ABLE TO LOOK AT IT AFTER INITIATING THE CLB. I RECOMMEND THAT PARALLEL; WINGTIP-TO-WINGTIP APCHS NOT BE ALLOWED AT SJC. IF BOTH RWYS ARE TO BE USED FOR LNDG; ACFT NEED TO BE STAGGERED SOME; EVEN IN VFR CONDITIONS. ALSO; ONE ACFT SHOULD NOT BE ALLOWED TO OVERTAKE ANOTHER ACFT ON FINAL. A SIMILAR PROC IS USED AT SFO WHERE THEY HAVE CLOSELY SPACED RWYS AND ARE BOTH USED FOR LNDGS AND IT SEEMS TO WORK WELL THERE. BY SETTING UP A DEFINED PROC FOR LNDG ON BOTH RWYS AT SJC; SAFETY WILL BE ENHANCED.