Spike didn't break Dru's neck. He pressed on her carotid arteries, (located at each side of the neck, under the jaw bone), until she lost consciousness.
In any case, this is a continuity error; in the first place vampires should never be able to lose consciousness, either from cerebral hypoxemia, (not enough oxygen reaches the brain), or a dramatic drop in blood pressure, (the heart is not supposed to beat at all!)
On the other hand, they of course draw air through their lungs because they can smoke. They can talk, (something has to make those vocal chords vibrate, after all!) They just don't need the oxygen.
Angel should have been able to help Buffy, because he should have had the capacity to fill his lungs with air, even though he didn't need it himself. The only argument that explains why he couldn't perform CPR is that perhaps he could only store a really shallow amount of air--maybe just enough to talk; that his lungs weren't particularly robust. That's definitely a bit of fanwanking but it makes it possible for me to watch that scene.
When Spike is "drowned" in season 7, I believe it's simply done as a form of torture; the First and the ubervamp know it won't kill him, but jeez nobody wants to have their lungs filled with water. It's also been assumed in the fandom that here is holy water in the mixture, thus adding to the torture.
So anyway, even if you explain the Spike stuff in season 7 and the Angel stuff in season 1, you can't argue that having vampires gasp for air and/or faint is going directly against continuity, if it's been established that they don't need oxygen. I just try to ignore it!