The thermal performance of loose filled cellulose compares well to other types of low cost insulation, but is lower than that of spray foam insulation. The thermal conductivity of loose-fill cellulose is approximately 40 mW/m·K (an R-value of 3.8 per inch) which is about the same as or slightly better than glass wool or rock wool.
Cellulose is very good at fitting around items in walls like pipes and wiring, leaving few air pockets that can reduce the overall efficiency of the wall. Dense pack cellulose can seal walls from air infiltration while providing the density to limit convection, when installed properly. Some real world surveys have cellulose performing 20-30% better at reducing energy used for heating than fiberglass.
Compared to closed cell, Polyurethane foam insulation (R=5.5 to 6.5 per inch), cellulose has a lower R-value per inch, but is much less expensive.
Cellulose insulation contains fire retardants providing up to 50% better fire resistance than fiberglass. During a fire, this could give you more time to reach safety.
Cellulose Insulation provides better sound dampening when compared to many other insulations as well. It also restricts air movement which could bring moist air into wall cavities where it can condense and activate mold spores.