I'm probably missing something obvious, but what use cases are possible with BTC but not, say, PayPal?

With PayPal you can pay for goods, receive payments for goods, transfer to an individual, receive payments from an individual, do it all in different currencies and transfer in and out of bank accounts etc.

Aside from the fact that the model itself is rather different, I can't think of any practical uses that can be done with one but not the other?

Edit: for clarification, I mean in the context of the parent's scenario of Apple taking their 30% cut of a transaction. Obviously there are plenty of reasons to use BTC over other payment methods.