Is one better than the other?
I've noticed that national banks seem to charge more (and higher) fees. Is that just me?
George's answer is excellent.
To expand a bit on "which is better", just based on my experience with a handful of regional/national banks and a couple different credit unions:
Many credit unions are small, local banks.
Larger credit unions have more resources to cancel some or all of those downsides, but then they have more fees.
Large national banks have branches all over, ATMs everywhere, are open at the supermarket on weekends and evenings, and have really slick online banking. You pay for this (sometimes excessively, it seems) in fees. When you have to talk to someone, you may be lucky enough to have a personal relationship with someone at your local branch, but you are just as likely to get a drone at a call center who is powerless to actually fix anything for you.
Everything I said above for small credit unions goes for small, local banks.
What's "better" or "worse" depends on which of those things above are more important to you.
A credit union is a cooperative financial institution that is owned and controlled by its members and operated for the purpose of promoting thrift, providing credit at reasonable rates, and providing other financial services to its members. Many credit unions exist to further community development or sustainable international development on a local level.
Basically, it's a bank owned by its members. For the purpose of your question, regarding fees, you may think of a credit union as a "non-profit" bank.
Credit unions may also be thought of as being similar to an utility (or other) cooperative.
To expand a bit more:
A bank, whether privately or publicly owned, is a capitalistic undertaking, intended to make money for its owners. A credit union is a more "altruistic" endeavor. They can not operate at a loss, but their reason for being is less about profit and more about helping its depositors; who are all part owners.