Cyrus, as you might have guessed, it depends. Sometimes credit union has better rates sometimes big banks.
Check the prevalent rates from different banks. There are many sites that provide a comparison (bankrates, lendingtree). Be careful, don't give out your phone number to lendingtree, unless you are ready to hear from 10 different banks with offers. What also helps is contacting a loan expert- if you have somebody who bought home recently, reach out to them and get their loan processor/expert.