Susan Tiffany, director of consumer periodicals for the Credit Union National Association, says that you shouldn't use a debit card online, since the debit card links directly to a checking account, you have potential vulnerability there she says.

If you have problems with a purchase or the card number gets hijacked, a debit card is "vulnerable because it happens to be linked to an account," says Linda Foley, founder of the Identity Theft Resource Center, she also includes phone orders in this category.

The Federal Reserve's Regulation E covers debit card transfers. It sets a consumer's liability for fraudulent purchases at $50, if they notify the bank within two days of discovering that their card or card number has been stolen.

Nessa Feddis, vice president and senior counsel for the American Bankers Association, says most banks have additional voluntary policies that set their own customers' liability with debit cards at $0 the protections don't relieve consumers of hassle. The prospect of trying to get money put back into their bank account, and the problems that a lower-than-expected balance can cause in terms of fees and refused checks or payments, make some online shoppers reach first for credit cards.

With a big ticket item, a credit card is safer. A credit card offers dispute rights if something goes wrong with the merchandise or the purchase, she says.