i love the movie, and Idina was the one who fully brought out every bit of Elsa's emotions in this song. Demi's version has its coolness but it jus wont fit if u r addicted to the movie/Idina/Elsa. jus can't.
To be quite honest I could never stand Demi Lovato's voice, not even as far back as her first days on Disney Channel. She sounds like she's screeching no matter what note she's pulling, in my opinion. Idina also sounds like she's yelling when she sings but it's a powerful way, not annoying like I feel Demi's is.
At the moment, I'd have to go with Idina' version. It's so powerful and moving that it just blows Demi's version away. In the future, that may change, if we take the view of what a lot of singers do, which is to perform the song with a different composition. An example of that is when they do an accoustic or "unplugged" version. In this case, we get that version along with the original version.
I feel Demi's version is more relatable - the added lyrics and repeating of the chorus make it a better fit to everyday situations, so I find myself slipping into it often. But Idina's is more powerful, more dramatic, it and she belong in the movie and I like it better. Also the orchestration is better.