If I go to straight with one line answer then credit card should be used for the payments.
The below are the reasons to use credit card rather than debit card.
If credit card is lost or someone used your credit card without your permission then you can recover your money. The payment made through credit card do not deduct money from your bank account immediately and you have almost 50 days to pay it. If you found that your credit card has been used illegally then on complaining this fraud transaction to the bank, you will not be charged any money and the money debited will be reversed to your credit card. However the money reversal back to your credit card can take 2 to 3 months but since you have not paid it so there is no money loss to you.
In case of debit card, this is nearly impossible to get the money back. Since the money is directly deducted from your bank account, so you do not have any time to take any action. If you are lucky enough that after making a complaint you got your money recovered, still you have to be without money for a long time until the recovery process completes which can take 2 to 3 months.
Credit card has other benefits if used wisely
The pay later option, which gives you almost 50 days to pay, is a great feature of the credit card. If you need to make any purchase and no money in your bank account then credit card allows you to fulfill your needs. In addition, the amount spend today will have to pay after a long time which is a good money saving technique too.
Time to time, credit card companies or shopping portal announces cashback or reward points on credit card, which is another great advantage of using the credit card.
Most of the credit cards offer free lounge access at airports, which is a most, loved feature used by frequent air traveler.
Therefore, if you have to choose credit card or debit card for shopping then certainly credit card is the best choice.