ACR PIC CONCERNED WITH CLOSE-IN RWY CHANGE AND SEQUENCING AT SFO.

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BAY APCH VECTORED US (ACFT X) DOWN THE BAY FOR A VISUAL APCH TO RWY 28R. HE TOLD US THAT RPT A FALCON (ACFT Y) ON VISUAL APCH TO RWY 28R AND WE WILL BE FOLLOWING THAT TFC. HE GAVE US A HDG FOR A BASE TURN. WHEN WE SAW THE FALCON; WE WERE RIGHT ON TOP OF THE FALCON AND ABOUT 4500 FT RIGHT OVER THE MARKER (BRIDGE). THEN HE CLRED US FOR A VISUAL APCH TO RWY 28L AND TOLD US TO MAINTAIN VISUAL SEPARATION WITH FALCON. DUE TO POS AND ALT WE HAVE; I HAD TO CONFIGURE THE ACFT QUICKLY AND DIVE TO CAPTURE THE GS. DURING THIS PROCESS; WE WERE LINED UP WITH RWY 28L AND HAD THE FALCON ACFT IN SIGHT AT ALL TIMES. WE NOTICED THAT FALCON ACFT SLOWED TO ITS APCH SPD. DURING OUR DSCNT; WE PASSED ABEAM OF FALCON ACFT. WHEN WE SWITCHED TO TWR FREQ; TWR CTLR ASKED US IF WE WERE TOLD NOT TO PASS THE FALCON ACFT. WE SAID NO; AND WE WERE NOT TOLD TO MAINTAIN FALCON IN SIGHT. SHE DID NOT MAKE ANY COMMENT AFTER THAT. I THINK PROB STARTED WITH BAY APCH CTLR. HE DID NOT INFORM US ABOUT THE RWY CHANGE AND OUR SEQUENCE. HE TURNED US TOO TIGHT AND HIGH BEHIND THE TFC. LATER ON; THE TWR CTLR TOLD US WE SHOULD NOT HAVE PASSED THE FALCON TFC. WE THINK SHE WAS WORRIED ABOUT OUR WAKE TURB DUE TO CLOSE PROX OF THE RWYS IN SFO. I THINK OUR UNDERSTANDING OF MAINTAINING VISUAL SEPARATION IS DIFFERENT THAN SFO CTLR'S. THEY SHOULD BE MORE CLR ABOUT CLRNCS. THEY SHOULD BE MORE CLR ABOUT CLRNCS. KEEP THE CREWS INFORMED ABOUT THEIR APCH PLANS.