Invest it.
If you're paying a monthly fee to have an account (basic checking or savings), then you're doing it wrong. I bank with Chase. Have been since early 90s. Haven't paid a monthly fee in years. I'm not sure about the specifics of your situation, but I suggest sitting down with a banker and ask them why and how to avoid paying service fees. Things like non sufficient funds, returned item, or over draft fees are common regardless of bank or credit union. If you're overdrawing the account, then set alerts that will text you your balance. Use features that are free (online banking and bill pay, mobile apps, etc.,.) to monitor and pay bills. You shouldn't be paying to do normal banking
As for the credit card? Well what kind of card do you have? Chase used to have this "insurance" on the card that said it would pay your bill in the case of your untimely death or whatever. Call the bank and cancel that service. It's not even offered anymore.
Long story short...there are ways to avoid paying fees while getting the best out of the account or credit union. You can't have a blanket statement saying "CUs are better than banks" or vice versa because it's such an individual experience.