Customers are owners.
The executive management of any company must answer to its owners. With a publicly-traded banking institution, shareholders care about only one thing: making money. In these companies, management often makes decisions that benefit the shareholder but inconvenience the customer. Shareholders might be happy when a bank decides to charge a new fee to increase revenue (and as a result, the stock price), but those who use the bank's services do not want additional fees.
With credit unions, the set of owners and the set of customers are one and the same. All decisions should benefit everyone.
Credit unions are non-profit.
Non-profit status means that more of the profits are shared with the owners/customers. That doesn't mean that the institutions can't earn a profit; any business needs to earn money to survive. The difference is that there isn't a pressure to find ways to make money off the customers. Additionally, credit unions benefit from exemption from federal tax, and that saved expense help more of the unions' revenue to be put to work.
There are fewer fees and higher savings rates.
As a result of the advantage listed so far, credit unions typically offer free accounts with no minimum balance requirements. Fees are generally absent from credit unions. Interest rates on savings, certificates of deposit, and some checking accounts often significantly exceed those offered by banks. In the same respect, interest charged for loans and credit are often lower. In fact, some credit unions are regulated such that the interest rate on loans and credit cards must not exceed a certain rate.