The corpuscular theory, first put forth by Sir Isaac Newton, contended that light was composed of tiny particles called "corpuscles". These particles traveled in direct paths, in straight lines. They also had a consistent velocity, and needed no medium in which to operate. In terms of destructive interference, I think the corpuscular theory makes more sense. If all these tiny particles are colliding with each other, that would negate, slow down, and even dissipate their energy levels as they interact with each other.
If we are talking about constructive interference, I prefer the wave theory of light. When the crests and troughs of two comparable waves overlap, you get a resultant wave that is the addition of the other two. I think the wave theory is the best fit for constructive interference.