There are several factors that impact what interest rate is available. On a personal level, your down payment, credit score and property type are the biggest factors. One a bigger scale, interest rates are set by investors via Mortgage Backed Securities. Two factors that are the most influential happen to be economic growth and inflation. The markets are set on the MBS level and then rate sheets are handed down to banks and mortgage companies.
To you, the borrower, that means your mortgage company or bank is not setting the market for the interest rates, and ultimately regardless of where you go, you’re going to get similar rates for most products. Not all banks and companies have access to a full variety of programs so it’s important to understand the dynamics of each individual program in order to decide if it’s the right fit for you.
One advantage that mortgage lenders and brokers have over your local bank, is that they see rate sheets from several investors, so they are able to shop your deal around and so who has the best program and rate for you as opposed to banks, who have access to their products and their products alone.