Also if we're talking about who is a more emotive singer. Again, I say Demi.
She doesn't write many of her successful songs but she certainly knows what she's singing about. She has an understanding of it and sometimes even her own personal connection to it therefore can emote into it as if she was the writer of it.
Your examples are of course Skyscraper but also songs like In Case, Heart By Heart, Fix A Heart, Mistake, My Love Is Like A Star. To say she hasn't got an emotive quality to her voice is a lie. She's one of the most emotive vocalists I've ever heard. It takes a very capable vocalist to emote into something they haven't written themselves.
Demi is a producer/songwriter's best friend. They need a voice like hers to sing their tracks.