Don’t know about the credit union you were using, but I can pay bills, transfer money to and from any internal or external account electronically with ACH transfers at the credit union I am using.
First, they’re different primarily in that they have different goals. Banks are for-profit and the goal of a bank is to make money for the owners, who are shareholders who’ve bought stock in the bank. They do this by lending out the money that their customers deposit at interest, and by charging fees to their depositors. A credit union is non-profit, and their goal is to make money for the depositors. They do this by lending out money at interest, and occasionally by charging fees to depositors (though they usually charge fewer fees than for-profit banks) and they give this money back to the depositors in the form of interest. Because they don’t need to pay dividends to their shareholders, they can often pay higher interest rates to their depositors.
Mostly this is a difference of philosophy. Banks are trying to maximize profit. Credit unions are trying to provide banking services to a community. I’ve found that I’m happier at a credit union.
As you’ve seen in this thread, there are a lot of people who are happier with a big national bank because it has branches and ATMs in lots of places. So credit unions band together so that their depositors can get services in lots of places, which makes CUs more competitive.