Add it up:
1) Buy your BART tickets
2) Possible wait for a train up to 15 minutes, expected value 7.5 minutes
3) Train ride 30 or so minutes
4) Work your way out of Powell station
5) Find an open cab around Powell station -- this alone can take time
6) Cab must potentially circle the block if you get into it facing the wrong way
On a relative basis, I would call that much longer, but I suppose it's a matter of semantics.
Another vote for the taxi, here. And I think your 30 minutes for the Bart ride is low. Isn't it closer to 40?
I live in the Lower Haight and drive past the airport every day, often during rush hour. It is 17 minutes from my garage to the airport exit in no traffic, and between 20-40 minutes in traffic. Downtown should not be tremendously different.