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.
It's like comparing the difference between a crystal of snow and a snowball. The particles from a haze machine are extremely small, where fog particles are much larger. This explains the main reason haze 'floats' longer and spreads evenly throughout a room. Particle sizes vary within each of these two categories. If dryness is a concern, the driest haze and fog is achieved with machines which use the pressure of CO2 to break up the particles to their smallest possible size.