I live in San Francisco, it's better (especially if you're 16). LA is huge and sprawling and difficult to get to places whereas SF is small and condensed, you move from one totally different neighborhood to another within blocks. There's tons of diversity, multiple methods of public transit which run often, run late and get you everywhere (bart which goes all over the bay area, muni trains, muni busses, other busses to go out to the other parts of the bay area, all night busses etc). Shows also almost always come here, maybe not exclusive shows like 1 appearance in the USA but we have multiple metal venues which are really cool and all ages and get every big tour that comes through here plus a really thriving and condensed local scene that has many venues it uses and everyone knows each other and parties.
The only downside for you would be getting a place to live. Cost of living in terms of apartment, food etc is extremely expensive so if you're 16 and dont have a job or money you could find yourself living in a shithole in the ghetto which can be very dangerous (most of the city is ok in terms of safe for a city but places like the tenderloin, hunters point, some parts of the mission district etc can be extremellyyy dangerous.)
All in all if you can afford it it fucking rules. Theres tons of metal and music in general, lots of nightlife, great partying, great schools, busses so you never need a car (I'm 19 and have 2 jobs, go to school and have a band and I almost never find myself needing to drive because the busses go everywhere and run so frequently), the weather is constantly foggy or cool so it never gets too hot but it never gets too cold, not a ton of rain; basically the weather is very mild and nice and the city is beautiful, diverse and has all the cool stuff I mentioned before.
If you have a choice between SF and LA I'd say definitely SF; LA is cool to visit for a super exclusive show and I love playing down there at all the venues but in general its just super expensive, really spread out, tons of freeways and the most insane traffic and can get really hot and miserable.