I think Hurt is way stronger than Bye Bye, not to mention that Bye Bye's video doesn't really relate to the song that much. The brief slideshows do, but pretty much everything else is either Mariah having a photoshoot or her and Nick Cannon having fun.
Mariah has a wider range ofcourse than Christina but I prefer Christina's voice and style of singing... some may call it screaming but she has a big and powerful voice and I love it... She sings with emotions too!!!