Obviously this poll is going to be a landslide, but for me FII is miles better, not even a contest. FII is my 4th favourite, Awake is about my 10th.
Awake is good up until Lie, then takes a nosedive into DT's longest solid waste of CD space. FII has a few stumbles, but overall it's a much more stronger album, much more energetic, much more emotional, much better production, much more variety, I just prefer it in every single conceivable way.
And the best of FII thoroughly beats the best of Awake (imo). And the low points of FII are still worlds better than the ultra low points of Awake for me.