I agree with roseaurora. I also read the Personal Correspondence, so that might be why. I thought SM made it pretty clear that Edward was the favorite for both Esme and Carlisle. As Roseaurora already pointed, out there are some quotes in the PC. In the outtake from NM (available on SM's website) where Rosalie calls Edward to tell him Bella is dead, she says Edward is Esme and Carlisle's favorite and they've both been miserable without him. Some of the conversations Edward had with Esme and Carlisle in NM, particularly when he was trying to decide whether or not to leave so he wouldn't hurt Bella, really showed how deep the connection and bond was. As far as Jasper, I also agree and would have pointed out the exact same PC quote roseaurora already did. Additionally, Bella mentioned that she got the feeling Jasper only stayed with the Cullens because of Alice. And, in BD, Esme was gushing over Alice when they returned, but no one really acted excited to see Jasper. I love Jasper, so that is not a criticism, it just goes to show that he was not as bonded with the family. So anyway my order of favorite children for Carlisle would be: Edward, Alice, Emmet, Rosalie. I excluded Jasper because I do not think they have a father/son bond, although they both care about each other and do have alot in common. For Esme: Edward, Alice, Rosalie, Emmet. Again, same goes for Jasper. But as compassionate and kind as Carlisle is and as sweet and nurturing as Esme is, I really doubt the difference is very noticeable; they are both caring and wonderful to all of the Cullens.
Do you think Carlisle and Esme view Bella as their child, on equal ground with the others? I know they liked her, cared about her, did a lot for her (protecting her numerous times, etc). But, did they view her as THEIRS or just as Edward's wife who they cared about and would do anything for IN ORDER TO KEEP EDWARD HAPPY? Before Esme met Bella, I think she encouraged Edward to kill her if that was the only way he could stay with the family; she didn't want him to leave them in order to protect Bella even if it meant Bella would die.