Water is very effective on class A fires (common combustibles like wood and paper). Halon is effective on common combustibles (although not as effective as water), but Halon is also effective on class B (flammable liquids), and it does not conduct electricity back to the extinguisher operator (class C).
Halon is similar to CO2 in that it is suitable for use in cold weather and leaves no residue. Unlike CO2, however, Halon does not displace the air out of the area where it is dispensed. Even for the toughest fires, less than an 8% concentration of Halon by volume is required, leaving plenty of air to use in the evacuation process. Also, unlike CO2, there is no danger of "cold shocking" avionics or other sensitive electrical equipment.
Dry chemical fire extinguishers are effective on A, B and C class fires. However, they are highly corrosive, and create billowing clouds of choking dust; dry chemical extinguishers should not be used in an aviation environment.