What's the difference between different quality pets?

I was reading this first-hand account of Pet Battles in Mists of Pandaria and found an interesting question the author wasn't sure about.

On the way back to Audrey, I caught a Black Lamb, a Squirrel, and finally the loathsome Stormwind Rat. The Squirrel is a rare-quality pet and the Stormwind Rat is a poor-quality pet, but I wasn't entirely sure what that meant.

What is the difference between different quality pets?

On the official Mists of Pandaria site they state:

Quality designates the overall strength of your pet's stats and will vary on every pet that you catch.

And in one of the blue posts this was elaborated on:

Pets that are captured in the world have varying levels of quality, just like an item would. The quality stat is randomly determined every time a pet spawns. Higher quality pets get a larger stat allotment each time you level. Be on the lookout for Rares!