What properties of light that can best be explained by the wave theory. What other properties can be explained by the particle theory?
Wave: Interference. Particle: photoelectric effect.
Young's double slit experiment is the classic proof of the wave nature of light. In the experiment light from two sources interfere. Particles are thought to be unable to interfere, but wave interference is well established by observation.
The photoelectric effect is the experiment that challenged the prevailing view that light was a wave (established by Young as above). There are several bits of detail to the experiment that confirm that light exhibits particle behaviour. The main thing to appreciate is that the threshold frequency and instantaneous emission of electrons support a discrete nature to light.
I recorded a video introduction to quantum physics in which I briefly discuss both Young's Double Slit experiment and the photoelectric effect. I hope it is helpful: