I don't know much about the matter but I read that the Amazon/Barclaycard row had been settled. I think that paying by credit, rather than debit card gives you additional consumer protection if things go wrong. I've never had to test this.
Not with Amazon, but, I have, once, had cause to “test” this. I had made an online purchase (£200 approx), using my Tesco Mastercard. Money taken from my account, but, no goods arrived. After chasing supplier, with no joy, I rang Tesco Customer Services, they sorted it, in this instance, I got the goods, after Tesco’s intervention. They (Tesco) did indicate to me that the supplier in question was “known” to them.