What are the main differences between cpap machines and oral appliance therapy?

CPAP most effective. But compliance rate is poor, about 40 percent. According to 2006 american academy of sleep medicine practice parameters, oral appliances are indicated for use in patients with mild or moderate obstructive sleep apnea who prefer them over CPAP and should be completed by a dentist with advanced training in sleep medicine.
CPAP likely better. CPAP is positive airway pressure that keeps the airway open while you sleep. When the airway closes you have apnea inability to breath, and you usually wake up to get a breath. CPAP is general more effective than either surgery or appliances. It takes some getting used to, but it is so effective it's worth it. Try earphones with low music to get used to it. You won't believe you ever slept before.