Whether one is better than the other is up to you. If you can carefully track your spending and stay within your budget, a debit card will cost less in terms of interest saved. Spending more than is in the bank, on the other hand, will incur hefty charges for insufficient funds, in the same way writing a bad check will. Another consideration is that the same features that make debit cards so convenient opens them up to fraud. If your debit card disappears, a clever thief can devastate your bank account quickly, and, while the bank is always willing to work with you, there is less recourse than with credit card fraud.
Stricter liability laws are in place for credit card companies. In the case of credit card fraud, you are liable for only the first $50, even if you don't notice it's gone until you get your statement. It's important to note that the law regarding debit cards is not the same. If you notify the bank within two days, your liability is the same $50, but after that, your financial liability increases exponentially as time passes. After the two days, liability goes up to $500, after 60 days, your liability can go up to 100%. Some banks have instituted voluntary limitations on customer liability, but not all, and they are not accountable to the same set of laws. It's in your best interest to know what your bank's policies are and how that applies to the potential loss of your debit card.
In addition to liability difference between a credit card and a debit card, credit cards also offer consumer protection on purchases; a built-in insurance policy against enroute delivery damage or defective merchandise.