As Hayden's internal thoughts don't start until his character in Awake is put under, there's no confusion as to what we're hearing.

It seems to be an old cinematic convention that internal thoughts don't sound like someone speaking out loud. (Unless a character is alone.) The alternative to the old echo gag is making the voices more like speaking softly.

http://www.youtube.com/watch?v=bIVzK-h6qao

Of course, if someone's been cryogenically frozen, they have no internal monologue anyway! ;)