First you have to understand the fundamental difference between the two. It is this. Using a credit card, one is in effect committing to a transaction with the intent of making good on the cost at a later date. A debit card has all of the benefits of a credit card, except that the money is being deducted directly from your credit card. As a result you can never spend more than you have.

On the other hand, a credit card has the advantage that you can get access to funds even if the amount is not in your bank account. This can be very important in the case of an emergency. With a good credit rating you may even be able to negotiate a higher credit limit, giving a greater cushion if needed.
So which is better? It depends. You need to consider a few things. Who is the card for? In the case of a responsible employed adult a credit card may be better. It allows him/her to have some protection if an emergency arises, knowing that the privilege will not be abused.
However, for an unemployed adult it may be wise to stick with a debit card. Spend what you have and no more. The same will probably apply for a college student who may not have much financial security of their own. Perhaps in this case, the age and maturity of the student could also be factored into the decision.
Having a credit card is in a sense a form of borrowing. Therefore, also consider your credit history. Do you have a problem controlling your spending? For those who do and perhaps have major debts to show for it, a debit card will naturally serve as a safety net.