The first time, we used Chase (we had accounts with them). We bought a condo in a new development.
Anybody who went with Chase but did not have any checking/savings accounts with them had their mortgage sold.
When we sold the condo and bought a house, we went with a mortgage broker who found us a great mortgage through a lending company. After 2 years, the mortgage was sold to another lender.
I think if you got with a broken, you have a chance at a better mortgage terms. But then many lenders that are not part of a bank have lots of negative reviews for poor customer service.