To me, 'let her cry' is chest voice...

I'm not sure about 'In the air tonight'. I'd sing it with my chest voice. I guess Collins does the same. Perhaps it just sounds that 'thin' because he has quite a weird voice :P

But I have to say, I'm no expert... So, I'm just guessing. Try to sing it the way which is most comfortable for you.
Are you using so little air that your voice is breaking into falsetto, giving it that whiny quality? Does your voice fill the room when you sing? It should.

Remember.... you should never be singing in just head voice or chest voice. It should always be a mix. I really hate those terms because they suggest a level of exclusivity.

Could I get some more talent in the monitors, please?

I know it sounds crazy, but try to learn to inhale your voice. www.thebelcantotechnique.com

Chris is the king of relating music things to other objects in real life.
they're both in chest voice, there probly some mix by phil collins at the end, the really high and raspy part. but its all chest