There really is no difference when it comes to a negative or positive from using your debit card or credit card to make online purchase.
However, we can say that credit cards will ALWAYS be the safer item to use.
Credit cards mean safety
Safety is the prime reason a credit card is always safer than a debit card.
If your debit card is misused, your account is automatically withdrawn from (possibly overdrawn), taking money away from you. With a credit card, your dispute puts the weight of the theft or misuse on your credit card company to handle, not you.
One additional benefit from using credit cards over debit cards
Usually, credit cards have program that allow you to receive points back for purchases. Purchases can accrue cash rewards, flight mileage points and other perks for their use.