Hi there Lexy!
The best thing you can do is to shop around and get quotes from four or five financial institutions. There isn't a clear cut answer to weather a credit union offers a lower rate than a bank. Sometimes they do, but sometimes they don't. It's really kind of up in the air which institution will give you the best rate. It would be better to just speak with a few and have them tailor a quote for you than to just get estimates on rates from ads.
Also ask the lenders about their mortgage process. Finding an bank or lender that meets your needs is key to making your mortgage go smoothly. Do you want to be able to submit documents online or check you mortgage 24/7? Would you rather turn in documents to a banker and be able to sit down with them on a regular basis. How quickly can they close loans? These are all things to consider.
Lastly, how low a rate you'll get depends on your credit score and your debt to income ratio. Have you checked your credit score recently? Do you have student loans or car loan under your name? You may see a low rate in an advertisement, but you may not get it due to these financial factors.
If you have any other questions please let me know! Good luck!
A credit Union would be your best bet. They usually have way lower fees than the big city banks. They're also smaller and have more time for their customers. Fees are usually lower with Credit Unions too.