The first replacement for St. Vibiana's, commissioned in 1904 by Bishop Thomas Conaty from the talented if presently underappreciated firm of Maginnis, Walsh and Sullivan, would have been a magnificent Mexican Baroque pile on Ninth Street, dedicated, somewhat oddly in the City of Angels, to Our Lady of Guadalupe, but the economic depression of 1907 caused this project to be shelved. Some suggestion of its potential splendor can be found in Spanish revival structures of the same approximate period, like the church of St. Vincent de Paul and Goodhue's work at the 1915 San Diego Panama-California Exposition.
The second was that of Archbishop John Cantwell, who requested a design from Philip Frohman, the principal designer of Washington National Cathedral, in 1945. The project is interesting more for its seemingly-late start date and ambitious scope than the actual architecture itself, which is a an agreeable if fairly conventional Gothic with only very tenuous regional associations. (While somewhat difficult to tell from the photo above, I have been told the Gothic chosen was derived from Spanish precedents.) Images of the interior I have seen show a rectilinear, rather austere, French Gothic ambience, neither stunning nor terribly offensive, but undoubtedly standing foresquare within the design standards of the American Gothic revival.
It would have stood on Wiltshire Boulevard and it would have been also called Our Lady of the Angels, as the present cathedral. Nonetheless, sadly, Cantwell's successor directed the funds, after convincing the donors to re-shuffle their contributions, towards a massive building campaign of new parishes and schools. Perhaps, if it had been undertaken, it might have been one of the last major building projects before the current incipient revival. Or perhaps not, given the fate of churches such as St. Mark's Episcopal Cathedral in Seattle, of which only a tiny stump was actually completed. The mind reels at the possibilities.
Source: Cathedrals of California.
