An independent accountant is someone who's not part of a chain. These accountants offer reasonably priced tax preparation services with a focus on personalized service and building an ongoing relationship.
If you need your taxes in a hurry, or want the convenience of dropping by an office without an appointment, going to a retail tax office is ideal. Independent accountants often work by appointment only, and popular accountants often schedule appointments a year in advance.
Both retail and independent tax preparers tend to charge about the same for tax services. So basically your choice should be based on your needs for convenience, location, and expertise.
Like with any other service, you should call ahead to find out what their price ranges are, and if they have time to see you. Above all, you should expect your tax accountant to be helpful, courteous, and knowledgeable.