I remember moving there, hearing talks about how international Zurich was, and then realizing most of those foreigners were German. :-) It's diverse on paper (and probably to the Swiss), but it's not like it's a cosmopolitan melting pot.
If you exclude neighboring countries Zurich has a foreign born population share of 27% (compared to 18% of Los Angeles). If you only look at the last 10 years Zurich has foreign born non neighboring immigration of 10% (compared to 4% for Los Angeles).
If you only look at intercontinental migration then Los Angeles wins with 14% (compared to 8% of Zurich).
So yes Zurich is less cosmopolitan then LA, but most of it is just because the US has more diverse neighbors.
It's way more diverse than Zurich. Well, if you mean "diverse" as "more brown people" as your comment seems to imply.