I'm a member of BECU, and I've loved credit unions ever since I switched to my first one.
I was previously at Bank of America and trying to buy my first car. I went in, filled out the paperwork, and waited 3 or 4 weeks to get turned down. I went in the next day to Verity CU and filled out the paperwork and was approved in less than an hour. My point is that most banks have all their underwriters, analysts, and actuaries in a different location than their banks, and usually the process for loans and other paperwork is a much longer process with a lot more 'red tape'.
Credit unions are "member-owned", so they are not for-profit like banks are. Banks have shareholders that they report to and are beholden to make a profit for.
I love that BECU has many great options for banking that don't involve going up to a teller (and getting charged for it like BoA did). I deposit checks easily at ATMs often with no envelopes or deposit slips, and can even deposit checks online by scanning them or using my phone.
However, one thing that credit unions don't have compared to banks are an abundance of ATMs and branch locations. You can find BoA ATMs and branches all across the U.S., but of you're a member of a credit union you will generally need to look for affiliate branches (pretty much any other credit union) unless you want to pay to withdraw money. Of course, if you're using your debit card then it really doesn't matter. Credit unions will probably not ever charge for using an ATM, debit card, or speaking to a teller, but banks will.