Bitcoin is significantly more private than credit cards. Credit cards, by their nature, are intimately connected to your real world identity. It's literally impossible for them to be private from third parties. With Bitcoin, even as it is, at least some degree of anonimity is possible regarding any person or organization that is not directly part of the transaction, although it often takes some degree of extra care.
Bitcoin is more private in that it is possible (arguably even simple) to conjure a pseudonymous identity that remains completely isolated from a human identity, with the caveat that such an identity must deal exclusively in BTC and digital goods, never sending or receiving real world goods (or their deeds) or fiat currency.
Bitcoin is less private in that once any goods or currency is exchanged at an interface, and a third party entity (could be a government, could be *anyone*) gains access to knowledge of that transaction, the identity of the *entire* networked history of that transaction is at risk of revelation.
This is why ZeroCoin is so critical.