In the US it's better to use a credit card even if you don't need to use the credit. The credit card company is on your side in any dispute and will reimburse you for fraudulent charges while banks don't provide that service for debit cards.
For instance, if a person used their debit card to purchase something from Nocturnal Readers Box, near the end of that debacle, they would be on the hook for the money. If they used a credit card, the card company would rule in their favor and reimburse them even if they can't get the money back from NRB.
Also credit cards provide other benefits depending on the card. Early tickets to events, discounts, frequent flyer miles, cash back, etc..