I have worked in all aspects of the mortgage lending arena: banks; big box lenders; independent broker.
Generally speaking, you can do better with a broker for the simple reason of overhead. Brokers focus on mortgage lending where Banks and Big Box Lenders are intertwined in so many different areas that the costs for each division tend to overlap.
If you choose to work with a broker, make sure that they can give you some references and they have a good reputation in the marketplace. Like any business, there are some good ones, and some bad ones.
I always tell clients to shop first and make sure you get ALL of the costs involved in writing then focus on the rate. If you would like to call, I'd be happy to chat with you.