First, the benefits. If you pay your credit card automatically, you will never forget to pay. Paying in full will prevent any interest and late fees from ever happening. This can save you money. If you forget and pay late, it will cost you a lot of money. Automatic payments are a safeguard.
The drawback, what if you forget that the payment is happening and do not have enough money in the linked account? If you have $100 in your checking and your credit card withdraws $110, you will get hit with a bank overdraft fee! That could be worse than a missed credit card payment depending on the circumstances.
Automatic payments are right for some people. If you keep a high balance in your checking account, automatic payments are right for you. If you keep low balances in checking and keep higher balances in a savings account and do a transfer each time you pay your credit card, automatic payments are probably not right for you.
I do not do automatic payments. I prefer two payments per month manually, as I discussed a couple of days ago. I do not make payments with checks. That is outdated technology. If you still do that, it might be time to sign up for Internet banking and online credit card accounts.