The reason why we deal with Anduin at the temple of the red Crane is...
Well, you're kinda surrounded by neutral Pandaren (who both need your help, offer gold for that help, and would beat the !@#$ out of you if you caused trouble.).
Even better? Anduins quests are both to help the Pandaren, and he -pays- you.
He -knows- you're Horde, and treads lightly because of it. He wants to mend relations, so that's why he doesn't run like a little sissy. He, through the power of gold and being a decent person, gets the Horde player to aid the Pandaren at the temple, and not the Alliance. He also accompanies the Horde player, and helps them with those problems, in good faith.
He's still considered very much fair game...but it just so happens that these Horde adventurers are more interested in getting in good graces with these new Pandaren. After all, if you make a good impression, you may get additional forces, perhaps? And rewards too!
And Anduin is not completely flawless. He has shown to make mistakes before. He went, alone, to face the Divine bell. And nearly got himself killed for that. He has little ways in Combat. He is a priest, through and through, and can only survive through diplomacy/healing. That's what sets him apart from Thrall. Thrall was powerful, and all loving, and so diplomatic. Anduin is only diplomatic...and even then, he is still only 15 years old, so he comes off as very naive. I think the only reason why Baine and the other leaders find him so charming, is that he's trying so hard to be mature, and all leader like at such a young age.
At this point, Anduins strength (his willingness to lean, his childish naivity) can also be considered a weakness, which leaves room for character development, both negative (he becomes jaded), and positive (he continues learning, and is able to lead better because of it). Thrall, on the other hand, is already self actualized, and even worse, we haven't seen much in the way of flaws on his end, which is what gives him the label of 'Authors pet'.