The wave-particle duality is not a quantum superposition like you're describing (which would break down under measurement), although the caricatured manner in which we teach it might lead you believe that. It's a little more simple than that.
In our world, we are used to two kinds of things: particles, and waves. We are used to this distinction, and describe most things in one of these manners. Sound is a wave, a billiard ball is a particle, vibrations are waves, bricks are particles. If something is a particle, it has certain properties, like position, size, and shape. If it is a wave, it has certain other properties like wavelength, frequency, and amplitude. In addition, there are some common properties like velocity and direction.
When it came to studying light (and many other quantum stuffs), we can't directly see what it's made of. But we can take measurements of each "puff" of light, and infer its properties that way. When we do this, we notice that puffs of light have some properties which are particle-like, and some which are wave-like. So the term "particle-wave duality" became popular to describe this new material that was behaving simultaneously like a particle and a wave. It doesn't make sense to ask which one it is - a "puff" of light is neither a particle, nor a wave, but a different kind of stuff which has some properties of each.