ContinueWith is fine for simple flows, but things fall apart when you need to perform multiple async operations with the same error handling. You either repeat yourself or you put the error handling code into a lambda and make sure you always pass it along.

Assuming you just want to propagate exceptions, you have to mess with TaskContinuationSource (I.e, promises) and be damn certain you have wired it into all the right places.

Async/await makes error handling much more uniform and "obviously correct" than stringing callbacks together.