Christina oversang, which she is prone to doing in normal performances.
I'm not a hater by any means. I love some of Christina's performances, and own a couple of her albums, but she is prone to singing as if she's determined to finish with the audience convinced she's a great singer, rather than leave the audience feeling they've enjoyed a good song, well sung.
It was always going to be dangerous bringing her in for a duet, because her normal style is near enough the opposite of what makes a good duet. Beyonce, on the other hand, knows how to sing like a diva, but also knows about harmonies and singing in a group environment, and has the grace to let another singer shine.
Rebecca was overwhelmed, and forgot to sing, and while that's not directly Christina's fault, her general demeanour was not condusive to bringing out the best in a nervous X Factor finalist. If you look at body language alone, the difference between her and Beyonce is enormous.
That said, I don't think Rebecca is as amazing a singer as some might think, and she's not as good as Alexandra was. She's still the best one in the competition, but she was coupled with a singer that would have outsung all of the other professionals too.
I think it's of note that Cher thanked Will.i.am for making her feel so comfortable singing with him. There was no chance of anyone saying that to Christina.