Air carrier on visual approach to Runway 28L for SFO initiated go around after receiving TCAS RA and observing Runway 28R traffic drifting into landing path; reporter suggesting ATC utilize staggered procedures during Charted Visual Approaches.

Narrative

We were on final to Runway 28L in KSFO;having been cleared for a visual approach and established on the ILS. An air carrier was on final and cleared for visual Runway 28R. As we got closer to the airport; having passed the bridge and slowed to final approach speed; the Runway 28R B737 traffic kept getting closer and closer to our aircraft. He was abeam us. The wind was light out of the North so at first I thought he drifted a little and would correct. I was hand flying the aircraft and drifted over to the south of the final to 28L as a precaution. About that time we got a TCAS traffic alert on the 737. Then the Runway 28R traffic got even closer and I banked left to keep away from him. Then we got a TCAS RA indicating 'Climb; Climb.' We executed a go-around shortly thereafter as we were not able to be on our final because of the Runway 28R traffic and of course had the TCAS RA. Both of us considered this a near miss. I called the Tower after landing and talked with the Tower Supervisor. He said the B737 pilot had said that he was on the LNAV approach and that the needles were crossed for 28R. He also said he understood why I went around. Then he said he would show it is a normal go-around. I think the B737 pilots were not aware of their position relative to us and perhaps had a LNAV error big enough to put them on our final. Suggestions; San Francisco Charted Visual Approaches should be conducted with a requirement for staggering rather than making it just recommended.