There was a constant palpable rivalry with both NYC and Southern California
Living in the Bay area, I can't say I relate all that much. You hear about New York in the context of food and finance, and about LA in the context of fashion and Hollywood. But not really in terms of a competition of some kind. Maybe it's a peninsula thing.
The upper-middle class isn't nearly as preoccupied with location. You don't really identify with a place if you can't afford to buy a house there. (Or, if you do, you're a sucker.) The NYC envy of the Silicon Valley elite is mostly a phenomenon of the VC/MBA circle. (I've never heard of L.A. envy. Maybe in the '80s or '90s it was strong, but I can't imagine anyone having that now.)
Living in the Bay area, I can't say I relate all that much. You hear about New York in the context of food and finance, and about LA in the context of fashion and Hollywood. But not really in terms of a competition of some kind. Maybe it's a peninsula thing.