Can anyone recommend a reliable moving company?

We are moving from Chicago, IL to Orange County, CA. We live in a two bedroom, two bath apartment and need a moving company to transport our stuff and possibly help with some packing and unpacking. So far, we have obtained one estimate from Mayflower but would like to compare the rate with some other companies. In addition, I have read on Yelp that Mayflower’s estimate and final bill are two very different rates, not sure if that is true.