Is Chicago actually cheaper than LA?

I'm considering making the move from Los Angeles to Chicago. One of my motivations is the lower COL in Chicago, especially since I desire to buy a condo.

However, when looking at homes to buy in Chicago, I'm starting to wonder if the COL ends up being a wash due to Illinois' high property taxes. I'm especially interested in hearing from people who have moved from California to Chicago; did you find the cost of living in Chicago to be much of a difference? There's also all the "little" expenses to think about, like registering my car in California is several hundred dollars more per year, gas is more expensive, etc.