I've lived in both, and I prefer Chicago.
Much depends, though, on what you want. It's rather a matter of taste. I like a real urban environment and changing seasons. Los Angeles doesn't feel like a city to me, and it's so spread out, with still rather limited public transportation, that you need a car (expensive to own there) and may have extremely long commutes if you can't afford to live closer to the sea than the Inland Empire. And though the weather does change with the seasons, it normally doesn't change much.
Then there are the earthquakes (you have to get used to regular temblors and prepare for the possibility of worse quakes), monsoon-like rains, mudslides, and Santa Ana winds that fuel wildfires. When the environment and climate go bad in LA, they go REALLY bad.
Finally, there's the influence of the entertainment industry, which tends to emphasize a sort of shallow glamour and superficiality that I, for one, didn't admire. It affects (I'd go so far as to say "taints") everything in LA.
Chicago is beautiful, with a knockout lake-front location, but the winter weather can be somewhat brutal, and we don't get much of a spring. We do have a gang violence problem, though it's largely confined to a limited number of areas. LA has one, too, but because of the way the city is spread out, gang violence tends to occur at a real distance from the more affluent areas. That's less the case in Chicago, but most of the city is is quite safe.
Chicago is considered an alpha global city and boasts world-class museums, an internationally-famed symphony, opera, ballet, and dance troupes, and a top theater and music scene. Public transportation here is extensive; you can live in the city without a car, and I know many people who do so. Chicago has also long been considered a important center for American architectural design, though LA has had its significant architects and buildings, too.
Both cities boast major professional sports teams, if that matters to you. I should add that LA also has museums and so forth, too, of course, but they are not regarded, nationally and internationally, as highly as Chicago's are. The LA County Art Museum isn't a patch on the Art Institute of Chicago.
Both cities also boast excellent colleges and universities, important to local culture, but Chicago is culturally deeper in a wide variety of ways. Again, the entertainment industry in LA is a problem.
Illinois and Cook County have high taxes, that's one thing you should keep in mind. You can be gouged a lot of ways here. People will claim there's a lot of corruption in Chicago, but having lived in Boston, Philadelphia, and Rome as well as LA, I don't think it's any different from any major city in that respect. Everywhere, people have their fingers in the urban pie.
So, as I said, it's largely a matter of taste. A real city vs. a sort of pretend city, though one that can be a lot of fun and is certainly warmer than Chicago.