When you are buying a home or refinancing it always pays to compare costs. I have seen clients that have talked to big banks and small mortgage companies. The numbers can vary depending on who the lender is. Some lenders tell you to compare APR's (annual percentage rates). However, those numbers are easily manipulated, so that's not the best way to compare costs.
Ideally if you are shopping lenders, you should compare numbers on the same day, at roughly the same time. Interest rates can change daily, sometimes more than once a day. Ask the lender to send you an estimate of costs. You want to make sure the costs are the same or close and the interest rate should be the same also.
I have had clients tell me that another lender quoted a lower interest rate and then as we compare, we realize that the lender was charging a lot more in closing costs. That may not be the best deal for you. We all want the lowest rates possible, but we also need to make sure we aren't spending too much in closing costs.
Sometimes clients aren't going to be in the home for too long - maybe only 5-7 years. Then it may make sense to use a higher interest rate and keep the costs lower. Most lenders can do an lender credit to pay part of your closing costs. Ask your lender about that. It will depend on your interest rate, but it's possible. It is similar to a 'no-cost' refinance - you are rolling the costs into the interest rate instead of paying them in cash or putting them in the mortgage.