The advantage of CCs in the US is that transactions are against your bank, not your money. Debit cards are debited from your account immediately, so you can't as easily reverse charges in the event of fraud, mischarges, etc.
But then, it is not that easy to defraud the EC cards, since you need the physical card to make a payment with them (in addition to a PIN that is usually needed to authorize the payment).
This can apply to online purchases as well. A charge from buying something from ebay, for instance, can be charged back if you end up not getting the item, broken, etc. It's probably harder to get your money back in a case like that with a debit card.
Thats certainly true. Usually, these cases are done with money transfers in Europe, which is not really reversible (on the other hand, this is where many people use Paypal, which also gives you the money-back feature of a CC).