In the US the credit card wins hands down, by federal law the credit card is responsible for fraudulent charges to your account. No such protection for debit cards exist, even if they are used as a "credit card."
A short, and unfortunately true, story to illustrate the issues with a debit card.
A man goes through a fast-food drive through and pays with his debit card. The cashier hands back his debit card, which is put back into his wallet for safe keeping.
The next day the man receives a call from his bank. His account is over drawn by several hundred dollars. After a brief discussion it becomes apparent that there where multiple purchases made with his debit card after the man nused his card at the fast food drive through window.
The bank explains that the card was stolen, the man disagrees, but finally takes his card out of his wallet. Right bank debit card, but not his name or number. It is a card reported stolen. The cashier at the fast food place switched the cards...
An expensive way to learn that debit cards are not protected by law.
- Only use your debit card at your banks ATM.
- Use your credit card for purchases.
- Your spouse or significant other should use a credit card with a different account/card number* on it.
* Most banks will issue a different card number for each card issued for an account. This allows tracking who spent what, and replacing one lost or stolen card while still being able to use the other card(s).