If by "automatic payments" you mean ACH direct withdrawals, the benefit is "I don't have to remember to pay my bill."

The disadvantage is "An outside entity can remove an arbitrary amount of money from my account at any time, keep it for an indeterminate amount of time, then return it without penalty."

I could see have a charge automatically applied to a credit card (where you're able to dispute it, if necessary). I cannot imagine why anyone would ever want to set up direct withdrawals.