If you're looking for an in-depth analysis on pet variety in Pet Battles, I suggest reading this blog article, written by Cavernshark: "Fly or Die – Status of Pet Battles in Mists of Pandaria Beta".
I admit I'm not much of a theorycrafter or one that looks that a system from a technical or analytical standpoint, so I can't exactly weigh in my thoughts on the matter of which pet family will be "easier" to level in the open world.
However, from my experiences on the beta, I'm finding that leveling a flying companion isn't any easier than leveling the other pets from the other family types. In fact, I found leveling a flying pet to be much more annoying, if anything. My current team make up consists of a rotation of Beast, Undead, Aquatic and Elemental.
Then again, I'm focusing less on which pets have a chance of dealing/taking more or less damage from different family types, and instead forming a pet team(s) with more synergy. If one pet has a certain ability that another companion would benefit from upon a switch out while in combat, I'll likely use them on my team.
That isn't to say that I haven't been aware of strengths and weaknesses of certain family types, but it's not as big a concern to me. Sure, if I run into a Beast and I'm currently using a Critter as my starting pet, I know that most of the Beast's attacks will be strong against mine. My Critter isn't completely at its opponent's mercy, though, and with the write moves, ability choices, and tag-team effort, things turn out in my favor.
But I feel like I'm digressing from the initial point which was the lack of pet variety during the leveling process. I definitely do agree that initially, you will run into mainly Beast, Critter, Aquatic, and some Mechanical and Flying early on, making some pets seem like the "go-to" for leveling. Whether or not sticking with only certain family types will work in the long-run is debatable.
I think the reason behind the low number of varying pet families in the world is the fact that the environment really dictates what type of wild pets you'll encounter, and Blizzard really can't go through and drastically alter everything for the sake of inserting more of a variety of pets.
As you progress and level, though, you are exposed to more of a variety, not to mention the Pet Tamers that you have quests to defeat do use companions that can sometimes be in the family type you normally wouldn't run into while leveling.
In the end, it will really be up for each player to determine how they choose to play Pet Battles. What works well for one may not work out for another. And I really do think that despite the possible theorycrafting and min/maxing, Pet Battles is shaping out to be just a fun minigame. Unlike in Pokemon where there was always that one ultimate pet that everyone had to have due to its overpowered nature, WoW's version truly is a 'play how you want to play, and you can still be just as successful' minigame.