As far as I've read, a credit card is generally better than a debit card. (Please correct me if I'm wrong.)
My question is should I also have a debit card? The downside is the added risk of the debit card getting lost or stolen.
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1) Some vendors, specifically utilities and rent payments, often will not accept credits cards for payments. While these can generally be managed through bank drafts instead, hiccups in payment systems happen, requiring alternative payment methods. This is where the debit card comes in handy.
2) Unless you are paying off your credit card every month, you are paying high fees on it. If debt is an issue, possessing a credit card can lead to greater debt issues over time.
3) Nearly every credit card I know of charges high fees for cash advances. Mine is 17% if I remember correctly (I never use it). Without a debit card, you either pay expensive advance fees, or have to go to the bank. Debit cards allow withdrawals without exorbitant fees (couple of dollars for out if network transactions usually). And for many banks, they have an "in network" atm system without fees.
Two issues I see with your question:
I've never seen a place that takes debit but not credit cards. Additionally, your bank may provide an ATM-only card that cannot be used as a debit card, but you have to ask explicitly for such an card without the debit feature.
You are wrong in your comparing of credit vs. debit card as 'better' and 'worse'. Those are 2 separate products, which looks similar, but are quite distinct.
While credit cards usually provide better facilities against fraud transactions, and additional insurances, it's not always the case, and debit cards can be used to pay in internet as well.
The biggest disadvantage of credit cards against debit cards are cash withdraw fees. Cash withdrawal usually results in credit being interested from the day of withdrawal, so you'll have always to pay interests. It's a consequence of credit card being an instrument designed for cashless payments, not cash withdrawal.
So which products makes sense for you depends on your use case. Most people profit from having both. Some people need none of them. If you generally pay with cash, you need debit card for ATM withdrawal. If you mostly buy in internet, a credit card might make more sense.