For myself, I have both debit and credit cards. I like using credit cards more because you get a little bit of an incentive to spend. Now the catch is that I only spend money on things that I really need, like groceries and clothes. I don't overspend, and spend in my limits. If you know what your limit is, you can make a couple extra cents by using a credit card.
I prefer using a debit card as it deals with my own money. The only reason I have a credit card is to establish and improve my credit. We only use our credit card in times of emergency or when we don't have cash on hand.
I stopped using credit cards altogether and if I ever do decide to get another one I wouldn't have more than one major credit card. While credit cards are nice for having the ability to pay something off over time; when you really think about it unless you're paying your balance off in full fairly quickly then you're actually paying for your purchases several times over. Personally I would rather save up my money and pay cash for the things that I want, which allows a person to actually save money, verses spending that money on interest fees.
I prefer the debit card because it helps with keeping money out of large impulse buys. It is harder to throw a large sum over all at once verse throwing it on a credit card and racking up debit. At the same time, there are some nice things about having a CC for various purchases as long as you can wisely handle the money.
As others have pointed out, it's easy to end up spending outside your means with credit cards, so be careful in this respect. Personally, I prefer using debit but there are certain advantages to a credit card - that is, it can build a good credit history which is used when you go for a loan or a mortgage in the future. Additionally, I believe there is added protection as a buyer with credit cards. For example, you use your credit card to buy a laptop online then the company goes bust - it's fairly easy to get your money back with credit card companies but more difficult if you use debit.
Mine is actually the opposite! I don't get reward points for my debit card at all, but my credit card offers rewards. So I end up using my credit cards for the points and then just paying it off before the bill is due so that I don't get charged interest. I wish my debit card had the same kind of program.
Honestly I prefer credit cards. As long as you use cc in a responsible manner and know how much you should spend up to each month, the benefits of credit cards are so much more than those of debit cards. Contrary to what you might think, credit cards are safer in that there's more precautions set up against them. And if you have a card with amazing service like amex, they usually refund all fraudulent charges and even reimburse you for refunds.
Wit debit card you can only spend what you have on the card nothing more than that. Personally I would have both of the cards and would only use a credit card when it necessary. I would limit myself to the debit card as it teaches you to spend only what you have.