It is better to pay your credit card off in full rather than carrying a balance. This is true for a few reasons. When you carry a credit card balance you will have to make interest payments. These payments can add up over time.
When you pay your credit card in full this can help to reduce your credit utilization ratio for that credit card. Paying in full also reduces the total number of accounts that are open with outstanding balances. Both of these things can help to improve your credit score.