You have protections under both systems (debit & credit), but the ones on the credit card are much more in your favor. With credit cards it's pretty hard to end up on the hook for the fraudulent charges (50$ limit on liability), while on debit cards you have to report the charges before a deadline.
Debit cards are always dumb. Think of it this way... if some skel gets ahold of your card and has a party, you’re stuck in a world of bureaucracy and problems. In my case, a stolen card or number on the 29th of the month means that my mortgage, car, possibly insurance, as well as one or more credit cards with automatic payment will be rejected for insufficient funds. I have a problem.
If somebody steals my Amex or compromises the number, Amex has a problem. I call customer service and wish them well.
With a charge card I can just make the purchase willy nilly and transfer out of my savings the exact amount of money I've spent all at once at bill pay time. If I get an unexpected charge then my mortgage doesn't bounce and I don't get hit with overdraft fees. Not only that, the statement only closes once a month, so I have a pretty significant interest free period; which is great if I'm fronting money for work expenses and have to wait for the reimbursement, for example.
There's also better fraud protection, rewards, and other benefits (rental car insurance, extended warranties, purchase protection, trip delay insurance, return protection, etc. etc.) that I don't get with a debit card but I do get with a charge card.
Your debit card use doesn't effect your credit score/history but using a charge card does since it still is a credit line, even if the loan term is very short.