Basically (as said above) since they don't have profits going to bank owners, there is more money available for interest to savers or lower interest to borrowers. Financially, you may be better off with a CU.
However, there may be drawbacks. With a nationwide bank, I can go in person at any time for any reason in any city of the US. If you have a small CU - tough luck. Same goes with 24/7 people operating phone lines, a good website, tons of ATMs, etc. I can get checks written from the same nationwide bank deposited in my account instantly instead of waiting 1-11 days (this has come in handy many times for me).
Of course there is nothing stopping you from being a customer of both. Then you get the best of both worlds.