Although both kinds of medicine are for coughs where a child is creating a lot of mucus that drips down the back of the throat, expectorants and suppressants work in opposing ways.
Expectorants trigger the cough reflex to help get mucus up out of the throat and chest.
A cough suppressant, on the other hand, blocks the cough reflex. When to use them is really a judgment call. I recommend suppressants when a child is unable to sleep because of a cough, since without enough sleep, his body won't be able to effectively fight the illness. Otherwise an expectorant might be helpful in loosening up his congestion. My best recommendation is to give your child a decongestant at the first sign of symptoms to dry up the post-nasal drip, which might help him evade the cough and chest congestion altogether.