Debit cards mostly give you the same protections as credit cards. They're worse in that the money comes out of your account immediately (but is supposed to be returned when you report fraud), and the rules are different and less favorable if your PIN is also compromised, but overall it's not too bad.

A compromise of your routing and account number for your checking account is potentially much worse. It's harder to take advantage of, but it's also much harder to fix.

(I'm not sure if you were treating the debit card as analogous to credit cards or account numbers, so treat this as confirmation/correction/elaboration/whatever as appropriate.)