Cellulose is wood fiber. More specifically it is ground up paper wastes (recycled cardboard, newsprint) mixed with boric acid and ammonium sulfate. It is relatively easy to apply in existing structures and is also cost effectivej, fire resistant and insecticidal (pests won't live in it). There are no health hazards known to exist from the application dusts. The disadvantage is that if you remodel a ceiling below, you have to remove the insulation. Also, there is no vapor barrier, so you may need to roll out plastic sheeting.
Fiberglass is available as loose blown in (like cellulose) blankets and bats. Also comes faced or unfaced (vapor barrier). Easy to re-arrange blankets and batts if you need to shift things around. Fiberglass dust is moderately hazardous to your health and can cause considerable skin discomfort in sensitive individuals. This is usually not a problem once it is sealed behind walls.
What is your application? New or existing construction, first or additional insulation?