Cost is the main reason people go to an independent, but there are other benefits as well. According to a Consumer Reports survey, consumers are significantly more satisfied with independent's than with dealers.
Most dealers have to charge higher fees to work on your car due to their expansive overhead. Just look at their facility and the amount of people there and think about who is paying for it. That is why their labor and parts prices can be as much as 25% higher.
Consumer Reports magazine recommends for you to take your car to a good independent repair shop for this reason, and only use the dealer for warranty work and recalls.