In the MSNBC Red Tape Chronicles blog, Bob Sullivan provides complete answers to this question. His answers cover two important points -- prevention and recovery -- related to fraud and identity theft:
"Fraud protection. Federal law affords credit card consumers better protection than debit card users. Credit users' obligation is capped at $50. Debit users can be on the hook for $500 if they don't report fraud within two days of learning about it and face unlimited liability if they wait more than 60 days. In practice, both debit and credit users generally enjoy zero liability guarantees from their banks, but those generous debit policies can be changed at any time. Consumer protection under the law is a safer bet."
"Fraud recovery. Getting money back in the event of fraud is much easier for credit customers than for debit users. When a criminal uses your credit card, all you have to do is refuse to pay for the fraudulent purchases. When a debit card is stolen, the money disappears from your account, and the burden is on the consumer to call the bank and get that money replaced. Anyone who's ever logged online to see a zero balance or been denied cash at an ATM after an incident like this will tell you that is no small distinction."
And perhaps most importantly for consumers burned by data breaches at retailers like TJ Maxx:
"When there's a big data theft, such as in the TJ Maxx case, you'll really wish you used your credit card. Even though the criminals don't have your PIN, they can still perform signature-based debit transactions with your card and drain your account."
Me? I use my debit card only at my bank's ATM machines and grocery shopping. All other times, I use cash or occasionally a credit card. In restaurants with table service, I use cash because the waiter/waitress takes your credit card out of your eyesight.