I know serotonin and dopamine are the main "happy chemicals" in your brain. What is the difference in the feelings/types of happiness they cause?

Calm vs. excited. The role of neurotransmitters in feelings is complex, but serotonin is involved in a sense of calm joy as from meditation or marijuana, whereas dopamine is related to a state of excitement- sometimes called the sex, drugs & rock'n'roll neurotransmitter, as from cocaine. Deficiencies or excess of each creates problems. See http://www.buzzle.com/articles/neurotransmitters-and-their-functions.html.
Neurorelief.com. is a website for the Neuroscience lab company. They specialize in measuring neurotransmitters and provide natural treatment protocols if needed. Peace and goodhealth.