First off, hunter pets' leveling has been improved in the latest beta patch, so that now pets have to get just 1/10th (10%) of the hunter's total experience per level rather than 1/6th (16%). That's a big improvement of more than a third off of pet leveling time, but considering that now our characters have a ton more experience to earn per level than they used to, and a huge part of that experience we get comes from turning in quests. Our pets were taking an incredibly long time to level up before, I'm personally not sure this improvement will be enough to give it that special "training a pet feeling" (if it ever could -- personally I would do without pet leveling altogether, but that's just me). Hopefully this still won't be so bad, since, as we already know, if you tame a pet any lower than that, it will automatically just jump right up to 5 levels below your hunter. Hopefully Blizzard will be paying attention and reduce the leveling time even more if it's still too slow, or maybe even, as Mania hopes, include quest experience in pet leveling too.
Secondly, "caster stats" on pets are at last going extinct. Many of us have, in the course of our travels around Azeroth, desired one nifty pet or another, only to find out that it was a "caster pet" with reduced stats, and far inferior to the regular pets. Somehow for ages now, beasts found in the wild with a mana bar haven't changed to regular pet stats when you tame them, and have basically been a waste of stable space (nevermind why in the world beasts would have mana bars). But now that is going to change! As Mania reported, and Ghostwalker confirmed, caster pets will be a thing of the past, and their damage will be brought in line with all the other pets of their family type.