A problem with debit cards is that they offer the fraudster access to current account, to the limit of what's in the account. Credit cards are possibly no less secure but they do have a spend limit. Don't have a debit card, don't want one.
Glad to report my credit card security people phoned me couple months ago to enquire whether I had really stayed at a hotel in Leeds that week, as its outside my normal spending pattern and miles from home - I had indeed been there for work trip but fair play to them for checking.