I never purchase items with a debit card. A credit card always beats a debit card if you are able to pay it off every month.
If there's a wrong transaction with a credit card, the company will 99.99% of the time immediately take your side, and all you have to do is click dispute, and the money is instantly credited to your account.
With a debit card, in the past I have had to go through a week or so long process to get fradulent charges removed.
Plus other benefits, there are perks like automatically extended warranty on purchases like this one (amex), and all sorts of discounts.