Well since I think my post in the San Diego general thread inspired this post I'll do my best to contribute
SoCal culture would be even more Mexican influenced than it already is. Immigration and cross border issues would have a completely different discourse in national politics when America's second largest city is dependent on workers crossing the border daily.
San Diego wouldn't be a military town, since the military presence was encouraged by city leaders in the early days to regain some clout after losing the commercial race with LA.
Likewise, North Island would be an extension of Coronado. Miramar would be the city's primary airport. DTSD as a whole would stretch further, covering the Midway district and parts of Golden Hill likely.
LA would be a much, much smaller city and might not even be the most prominent city in the LA basin. With relatively little trade going inland Long Beach would probably be economically dominant.
Either Long Beach or Oakland would be the Navy's primary west coast homeport, with the latter being more likely. It's unlikely SF would be the bastion of liberal culture it is today if that happened.
It's likely the LA region would still be a hub of aerospace manufacturing, even moreso than today. If the Navy didn't move into Long Beach, the Air Force certainly would move into the Inland Empire in the 1940s for the good flying weather. But it's possible that we wouldn't think of the IE and the LA Basin as parts of a large whole as like we do today.