Barberry
Much better to use the cool mist vaporizer. If there is inflammation with the cough, and the cough turns croupy (which is common in little people with very small airways), the cool mist is much more effective at reducing that swelling. It's also safer in regards to the kids touching it or getting too close to the mist. I prevented many croup attacks using cool mist for my kids, and elevating the head of their mattress just a bit, and I highly recommend them.

brokenarrow
Everyone has a preference, personally I like the warm humidity (steam), especially for a loose, congestive cough. The humidity wets and loosens the mucous in the bronchial tubes and lungs and promotes a better cough. Sometimes the cool air will irritate and restrict the airways.

Kee
It depends on what you are treating. If you are wanting to help thin the secretions, a warm humidifier is better. It increases the relative humidity in the air better than a cool mist. The warm air is able to hold more water molecules thereby adding greater water content into the air. When using warm humidification, cleaniness becomes an issue. Warm moist areas are breeding grounds for bacteria, so make sure you follow the cleaning instructions. If the child is suffering from inflammation, than a cool mist may be better. It won't humidify as well but it may help soothe irritated tissues to some degree. . Realize that neither option will work as well as the humidifiers in the hospital. Those are designed to be used in close contact with the child's face so more humidity is able to reach the airways. Another option for adding warm humidity, is to place the child with you in a steamy bathroom. Run a steaming hot shower and stand in the bathroom with you child. Do this a few times a day. As always, check with your child's doctor. There are also usually nurse advice lines that you can call to get advice as well. Check with your local pediatric hospital.