The scenario would be for a millennial. No car is required in the Bay, but is a car a necessity in LA? Is it a wash because rent is cheaper in LA, but you would then spend on car/insurance etc?
A car is a necessity in LA.
It’s handy in the Bay Area, but it’s possible depending on where you live to go without one. In the heart of SF it’s possible. In other areas of the Bay Area it’s pretty hard.
You don’t need a car in Los Angeles if you live and work in DTLA. Uber and public transportation are reasonable options. There are numerous sites for Zipcar rentals. Public transportation to LAX is tough.
There are 2 viable places to live in LA where a car isn’t a requirement, West Hollywood and Long Beach. Both have (really) amazing public transportation that is reliable and can get you to many other vibrant places, including the beach and all sorts of fun venues and activities in Downtown LA. I have (younger than I am) friends who live in both, and they do not use their cars (yes, they have them) about 50% of the time. One friend uses his car for work, parks it Friday afternoon and doesn’t touch it again until Monday, utilizing the Metro, car share services, and his feet exclusively. He is currently talking about selling his car, as it’s really not adding anything other than expense to his life. Add Lyft and ZipCar into the mix, and depending on work/school, a car is almost unnecessary. I personally believe if I lived in either of those communities I could absolutely get by without a car.
I don’t currently live in CA but we did live in the East Bay for a while, and DW and I frequently return and have some thought of retiring there—if we can afford it, which is a big “if.” So we pay close attention to the cost of living.
According to bankrate.com, the overall cost of living is 4.56% lower in LA than in Oakland/East Bay. Biggest difference is that home prices are lower in LA. But according to this source, average apartment rent is actually 27% higher in LA, That seems to shoot down a major premise of your question. I’d take these figures with a grain of salt, however, because in both areas the cost of housing is going to depend on exactly where you live. Low rents and low home prices in some pretty undesirable areas bring down the metro-area averages.
You can probably get some sense of the housing market in both areas by looking at online listings of apartments for rent and homes/condos for sale in desirable locations. If your millennial is seriously considering doing without a car in the East Bay, “desirable” would include areas with good access to public transit, because many parts of the East Bay aren’t well served in that regard. The BART system is OK but showing its age, and it’s mostly designed to funnel people into San Francisco; as local transportation in and around the East Bay it has limited utility, in my opinion. And the bus system is adequate, but nothing more. Bicycling is very popular in the East Bay, and it’s a cheap and pretty efficient mode of transport year-round, though there are days in the winter rainy season when it’s less than ideal. I biked a lot both as a commuter and for recreation when we lived there and I also made frequent use of public transit, but we also had a car which made the entire SF-Oakland metropolitan region and some incredibly beautiful nearby areas accessible to us. So for me, having a car would be a huge quality-of-life upgrade, even if you commute primarily by bike and/or public transit.
I think LA would be cheaper than the Bay Area. And, yes, a car is probably a necessity unless you are living and working downtown or can make it work with the Metro/Bus system and/or and Lyft/Uber. Likewise, getting around San Francisco and the Bay Area with only public transportation can be a challenge, too.
The only parts of the East Bay where you could get away without a car is if you lived close to a BART station, or a ferry pier such as Richmond. Your work place would either be remote commute and/or a place that is BARTable.
Living in SF, you would have a lot more chance to get by without a car.
You could be a totally green guy like my brother in San Jose and only depend on bike, foot and bus, but most buses are inconvenient and depending on area, dangerous.
The Bay Area, and LA are vast areas so you would have to provide more info.
OakTown has a huge range of housing prices, alto the safety in East Oakland can be questionable. Ditto LA. Nice areas in both will be pricey, but with LA being massive, you can find places that are not so bad. Of course, anything near public rail transport will have that factored into the price.
In most places in LA you need a car. In the Bay Area there are some public transit options (Caltrain, BART, buses and Muni in SF) but a car is still a necessity for many people.
As a sweeping generalization I’ll say LA is less expensive. The reason is the sprawl. There are a number of job centers so you can live within a reasonable commute distance of work in a regional center such as Irvine or the San Fernando Valley at a price that is less than a similar commute time in the Bay Area since the employment centers up north are more concentrated (bidding up closer-in apartments)
My son who works at Google in Mountain View does not have a car. He uses the Google bus to go back and forth to work and otherwise uses Lyft/Uber or takes the Caltrain to go to SF. Right now he’s sharing a reasonably-priced 2-bedroom apartment with someone who has a car, so they’ll often go grocery shopping together. I live in suburban LA and I think it would be difficult to live here without a car.
I don’t agree with your premise that a car isn’t necessary in the bay. Our daughter lives in Sunnyvale and works in Mountain View, and she absolutely needs a car. I think they only option for going without a car is if you lived AND worked in San Francisco.
btw people who live here don’t call it “Cali” 
Whether a car is necessary depends on individual factors like:
a. Where you live.
b. Where you work.
c. Where you do other things outside of home besides work.
d. Your walking and bicycling range.
e. Non-driving transportation (e.g. public transportation, company buses) coverage for a through c above.
f. Ability and willingness to use rental cars and taxi / rideshare services.
g. Whether you commonly need to bring large or heavy items with you to work or other places.
Definitely possible to live in many parts of the Bay Area without a car but you will pay a premium for a car free lifestyle. Even in the East Bay or other areas outside SF itself, rents reflect the huge popularity of locations that are close to transit and/or easily bikeable.
If one likes to hike or see the ocean or explore the surroundings, one would want a car in the Bay Area.
^^^This. Beyond shopping and commuting to work, a car (rented or owned) will more than likely be necessary in the SF Bay Area. You certainly can live near CalTrain, BART, MUNI, AC Transit, etc., but realistically, if you have any desire to explore the Bay Area, Santa Cruz, Monterey/Carmel, Napa/Sonoma, Tahoe, Marin County (Stinson Beach, Point Reyes), etc., a car is handy.
Even grocery shopping in the Bay Area is difficult without a car unless you’re in San Francisco. Especially if you’re in South Bay/Peninsula where there’s no BART or Muni, and only the Caltrain is reliably scheduled (and even then not really; the weekend hours are pretty sparse and delays are common). Buses in South Bay (VTA) are slow and a little uncomfortable outside work commute times. At the very least you need a friend with a car, or have a Zipcar nearby.
Most of the Bay Area is bike-friendly though it depends on where you’re trying to go. I’ve also driven by a couple of car vs. bike fatalities when I used to live there so when things go wrong, they really go wrong.
Or I guess you can use the errand services or get everything shipped to your door…
I am a Bay Area native, my family still lives there but I have lived in LA since I finished college. LA is cheaper for an equivalent housing situation. You can get by without a car in LA but it takes dedication. But what prompts the question? If you’re comparing two schools or two jobs, a more specific location for each would get you a much better answer. Beverly Hills is not Irvine and Oakland is not Palo Alto but each pair of cities belongs in the same region of Ca.
I’ve got to disagree with this one. Oakland and Berkeley are extremely bike-friendly, and when we lived there I found it very easy to do grocery shopping on my way home by bike, both at the Berkeley Bowl (a spectacular independent grocery emphasizing organic and local products, with a truly outstanding produce section) and at some really nice specialty shops in both cities. Easier than a car, actually, because the parking is so limited. If you’re doing all the shopping for a family you might need more cargo space than you get on a bike, but for a young person shopping for one, a bike would do just fine. Up in the hills or in some outlying communities would be more difficult.
There are thousands of young people living in Oakland and Berkeley without cars. Many attractive and highly walkable neighborhoods are packed with local shops and restaurants----and they have limited parking, making car ownership a bit of a pain. There are also ample bike lanes and “bicycle boulevards”; BART and AC Transit are serviceable for some public transportation needs; and many people find several trips a week by Uber or Lyft to be cheaper and more convenient than owning their own car. And there are always car rentals for those occasional oceanside or mountain adventures. So going car-free is definitely an option. But housing is pricey in the neighborhoods most amenable to a car-free lifestyle.
LOL. I’ve got a son in Mountain View who is now working in Sunnyvale. Doesn’t have a car, doesn’t drive. He takes Googlebus to work. The grocery store is across the street. He takes public transportation to the airport, but honestly his income is such that it could cover Uber or Lyft, but he’s a computer guy and doesn’t really have much interest in exploring his surroundings. When he was furnishing his apartment (mostly from Ikea) he had stuff delivered.