CORP KING AIR CLB THROUGH OCCUPIED ALT AFTER TFC ADVISORY GIVEN.

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WE WERE RECEIVING VFR ADVISORIES. CTR POINTED OUT A B747 AT 10 O'CLOCK AND WE BEGAN TO SCAN IN THAT DIRECTION. HE WAS IFR AT 16000 FT AND OUR FLT PATHS WOULD HAVE TAKEN US DIRECTLY THROUGH HIS WAKE. WHILE WE HAD HIM VISUALLY; WE ELECTED TO INITIATE AN IMMEDIATE CLB ABOVE HIS FLT PATH TO 16500 FT. WE MAINTAINED VISUAL SEPARATION FROM THE B747; BUT APPARENTLY HE GOT A TCASII ADVISORY BECAUSE OF OUR DECISION TO CLB AND SUBSEQUENTLY HAD TO WRITE UP THE INCIDENT. HE SAID HE WOULD NOT HAVE CONSIDERED IT A NEAR MISS; BUT BECAUSE OF THE COCKPIT RECORDER WOULD HAVE TO FILE PAPERS WITH HIS COMPANY. THE B747 PLT THOUGHT WE PASSED UNNECESSARILY CLOSE. I THINK; BEING THAT WE WERE VFR AND HE WAS IFR; CENTER SHOULD HAVE VECTORED HIM AWAY FROM OUR FLT PATH; BEING WE INITIALLY HAD ONLY 500 FT SEP AND HE WAS A HVY JET. AT THE TIME WE FELT IT BETTER TO CLB THROUGH HIS ALT BEING WE WERE BOTH OPERATING IN VMC; THAN PASS DIRECTLY THROUGH HIS WAKE. POSSIBLY CTR COULD HAVE SUGGESTED A HDG TO PREVENT US FROM PASSING SO CLOSE IN THE FIRST PLACE. OUR FIRST TFC ADVISORY WAS TOO LATE FOR US TO ALTER COURSE WITHOUT MAKING AN EXCESSIVE BANK WITH PAX SO WE ELECTED TO CLB. SUPPLEMENTAL INFO FROM ACN 314743: WE PICKED HIM UP (TRAVELING WBOUND INTO THE SUN) AND IMMEDIATELY CLBED TO ABOUT 16700 FT ABOVE HIM USING NORMAL MANEUVERS CLBING ABOUT 1500 TO 2000 FPM. ACFT 2 WAS IN SIGHT AT ALL TIMES AND WE ESTIMATED HIM TO GET TO WITHIN 1 TO 1.5 MI FROM US AT THE CLOSEST POINT. I CALLED ZBW WHEN I GOT ON THE GND AND TALKED TO A SUPVR. HE DID NOT BELIEVE THERE WAS ANY CONFLICT NOR DID THE ACTING CTLR; WHILE WE WERE FLYING; STATE IT WAS A NEAR MISS. I THOUGHT IT WOULD BE BETTER TO CLB UP AND OVER AND BACK BEHIND THE B747 TO 15500 FT INSTEAD OF DEALING WITH WAKE TURB AVOIDANCE.