You get roughly the same level of fraud protection on both at this point. This is both due to converging legal protections in many places and due to market developments (both Visa and Mastercard require issuers to offer "zero liability" on debit cards just like on credit cards).

One advantage of credit cards is that you don't have to wait until the dispute has been at least accepted to get your money back, though.

You still get a 30 day interest free loan. Assuming you pay the full balance.