Without haze between the source of light and the subject, you have an absence of light, which is a real shame after spending so much on a good lighting system. Lighting without haze is like a message without sound equipment. Haze actually draws colored and white light through the air, creating a three-dimensional effect. Now, there are ways to have odorless haze that is only visible to a congregation when they see beams of light shooting through the room. This opens a whole new world of possibilities which were never before considered.
Fog is more dramatic.
It can be used to obstruct vision, which is why many magicians choose fog over haze. Because fog is very visible, you can immediately see the sharp division of where the fog begins, ends, and travels. However, if fast disappearing fog is essential, then a water-based fluid should be your choice. Fog creates a marbling or curling effect in beams of light, where haze creates a solid light beam. Particle size is the key difference between haze and fog.