Her cover of "The Scientist" is very good. It's different enough to work on its own, I think. I like the lighter piano, but maybe it gets a little heavy with guitars at the end.
I think Coldplay's "The Scientist" is under-rated because it's pretty. Coldplay can't help making pretty music. But the ideas brought up in the song matched what I was writing about when I first listened to it over a year ago, so this song impacted me a lot.
"Questions of science, science and progress, do not speak as loud as my heart..." is, although simplified here, a really really powerful idea to me, the idea of what's really important in this "civilized, technological world." The raw thrusting of the piano is at once dramatic, sexy, very intimate, and brings out the sadness in the lyrics.
The idea of going back to the beginning, and going in circles (he references a spinning coin, and how it can land on heads or tails) is a powerful backbone of the song's structure.
But I could never convince anyone who doesn't like the song that it's good. Where I see honesty, many see sappiness. Plus then they made it a single and had all the little girls singing along in the car, etc. I think that lead to it being dismissed too early by many people.
But I think Aimee Mann herself sees what I see in the song, which is why she's praised that whole album as one of her top ten to get and why she covered the song. As for which version is better, that's just totally up for grabs because they're both good as far as I'm concerned.
Sorry I wrote so much, I just like the song.