I sleep with the mouthpiece.
I went to some fancy sleep doc who did a sleep test on me, said I had mild to moderate sleep apnea. HIS EXPLANATION was that tooo many doctors just throw guys on CPAP's without looking at the other options. He suggested I get this molded mouth guard that holds your lower jaw forward, in turn, opening your airway more. If I hated that, I could always get a CPAP and end up having BOTH....if you get the CPAP FIRST, then want the mouth guard, insurance will take that CPAP away from ya. They only want to pay for 1 treatment.
But the mouthguard works really well, especially for me. If I go CPAP i need the full face mask because of my deviated septum (my girl is pushing me to get a CPAP).
Either way, try the mouth guard first THEN go CPAP.