Exactly, paying with a credit card is more anonymous than paying with Bitcoin. With the former, only the CC company, the merchant, and presumably the government can see what you purchased. With Bitcoin, anyone with a blockchain explorer can see your when and how much you transacted.
That's a bit inaccurate, your identify isn't attached toe the Bitcoin public ledger. It also has to be inferred through 3rd parties such as your wallet or some BTC exchange.