Too many factors for a simple answer. Nothing unique here. It depends on the particular facts and circumstances.
Huh? Owning versus renting? You mean, which is economically better, disregarding other factors like cash flow, stability, flexibility, etc?
“It depends on the particular facts and circumstances”
Here you seem to be comparing “stick built” with “factory-built.”
“It depends on the particular facts and circumstances.”
I’d say this is such a personal decision as to be meaningless to ask for advice from an internet forum with no special link to southern California.
Finally, one I can answer. In my experience, government codes define a mobile home as a structure, blah blah blah, built before HUD code took effect in 1976. Cities can and often do ban these due to there being no way to ascertain the quality (safety) of the structure.
A “manufactured home” is the equivalent blah blah blah thing but built after 1976 and conforming to federal HUD building codes, and therefore local governments may not regulate them in the same way (because federal codes trump local codes, basically).
And you didn’t ask this, but “modular” housing and “tiny homes” are also similar things, but they are regulated by local and state codes (each perhaps with unique quirks that must be satisfied).