I wrote a guide about this topic. Go to: http://www.brightscope.com/financial-planning/advice/guide/1398/The-Benefits-Of-A-Credit-Union/# I spell out the benefits of a Credit Union.
I have found "better" to be relative based on concerns someone has. I have been a credit union member for over 25 years, but never realized LL the benefits until a few years after I joined. Andrew's guide is very accurate, especially when it comes to service. My experience has been that credit unions usuall provde more competitive interest rates (lower on loans, higher on savings) than banks because of their mission.
To specifically address your question re: a car loan, I'd like to relate my experience. At my credit union, they offer a car buying service. I found they were able to negotiate a good price for the car I wanted. Perhaps I could have negotiated a slightly better price, but it would have taken a lot of time and I had to replace my old car. Next, their auto loan rates were better than the local banks at the time. However, since I used their service, the rate was even lower. I saved time, money, and got a better deal than at the bank.
Good luck with your auto loan.
Neither is inherently "better." Each will offer unique features or services to meet your needs. Personally, i bank where it is most convenient for me to do banking.