First off I have found several different definitions of duality and complementarity, so if anyone has a clear idea on what it meant with these terms please do share.
Now, what I mean is the following: in the wave-particle picture for light and for massive particles, can all phenomena be interpreted in both pictures, or do certian problems rely exclusively on one picture?
In physics, complementarity is a fundamental principle of quantum mechanics, closely associated with the Copenhagen interpretation. It holds that objects have complementary properties which cannot be measured accurately at the same time. The more accurately one property is measured, the less accurately the complementary property is measured, according to the Heisenberg uncertainty principle
On the other hand, the wave–particle duality is the concept that every elementary particle or quantic entity exhibits the properties of not only particles, but also waves. It addresses the inability of the classical concepts "particle" or "wave" to fully describe the behavior of quantum-scale objects.
To answer your question more specifically, any quatum system exibits both phenomena simultaneously, so they are not alternative interepretations of the same phenomenon, but rather two different characteristics shared by any quantum system.
The second answer is correct, some problems need wave-treatment, others may be treated with the particle approach.
Let's make clear the specific of each case: in the quantum theory an object (which typically is microscopic) is described by a wave-packet. In some experiments, and for some particles, this wave-packet is small (we say in this case that the particle is well-localized).
As long as we pass it through beam-splitters, but we just examine its passing through bubble chambers or ionization chambers or different materials, we may be able to treat it as a particle. Also, when the object is big, i.e. its linear dimensions >> wave-length, we can treat it as a classical object.
But if the wave-packet is sufficiently long, and we pass it through a beam-splitter, e.g. Mach-Zender beam-splitter, the two instanciations of the wave-packet meet on the screen at the exit a sufficiently long time for producing an interference pattern. For understanding why packet-length is important you need to read about coherence length.
Now, there is also another issue about particle vs. wave behavior. Even if the wave-packet is split into two, i.e. a transmitted and a reflected packet, when you place detectors on the transmitted path and on the reflected path, in only one of the two detectors will be produced a click. Only one of the two wave-packets gives a response. Why? The particle is one, we have a single particle, not two.
Do you understand how it is possible, why one wave-packet gives a response and the other doesn't? Don't you understand? Well, welcome to the club! Nobody understands! The quantum objects behave in a strange way. And though, this is the answer, the particle is one. This is also a particle-like feature of the quantum object.
Good luck!
