In seats, United is the clear leader with more than 2,100 seats each direction. Southwest Airlines operates 1,573, assuming that all its 737s on that route have 143 seats. American has 900 to 960, depending on the seating capacity of its Boeing 737-800s.
This may technically be true if you only count SFO-LAX, but if you count other airports (OAK, SJC in the north, BUR/ONT in the south), WN probably has at least 3x the daily passenger capacity of UA between the bay area and Los Angeles.