I would guess cloning is faster, because:
When you clone you create an object from another by instantiating it and it attributes.
When you use streams you serialize an object and deserialize it (whereas Java also have to create an instance of the object). So when you use streams you have the overhead of serializing the objects.
Of course the implementation of clone() should not do something unusual which increases time to copy the objects. To clone an object with arrays, primitives and Strings should not consume so much time.