In regards to fraud, you have the same protections regardless of how you make any electronic payment in the US (Reg E). A credit card could give you more protection if, for example, they offer to give you a warranty over and above the manufacturer's.
I got a call from my bank (where I also work) this week regarding fraudulent activity on my debit card, but there wasn't any. Normally a large company will save face and say there was a breach- if only to lessen law suits.
Zappos also had a huge security breach this month.. Maybe everyone that buys coachella tickets also buys shit from zappos?