The alliance has significant advantages in gaining that achievement, IMO. Balanced, hmph.:
The one pet I couldn't wait to get was the Sprite Darter hatchling, and when I was the right level, I ran out to Feralas and couldn't find a quest giver for the Horde. That's when I found out that the Horde cannot get that pet. If there is a pet that the Horde can get that the Alliance cannot, I have no idea what it is.
I have the white cat, which I bought with my draenei and then transferred through the neutral AH. I have the Westfall chicken too, but that was a pain to get. I thought I could just buy the special feed corn and transfer it through the goblins, but then no amount of clucking on my part would give me the quest. So I had my daughter run her little level 8 gnome out, do the quest and not loot it so I could grab it. So right there there are two quests that the Alliance can do that the Horde cannot, but at least the chicken is lootable.
I tried to grind for the disgusting oozeling, but I have such a low tolerance for it. The only Outlands pets I have are Miniwing from the quest, and the mana fry. I'd like to get the tiny sporebat.