I know this an old forum however I myself noticed the whole breed thing after I installed an addon and it has
OPENED MY EYES! Not all pets are great p/p or s/s or w'e. For example a pet that an "extra hit if goes first" important to have speed, a pet that has stun important to have speed.
I use the (S/S) Flayer Youngling, he does "kick" if it goes first you stun your opponent useless if he isn't, at (S/S) he is 325 so that's up there on speed, flyers are usually faster and those encounters suck. I got 2 other rares before it, released both because I wanted (P/P) and I was NOT going to waste a stone on something so easy to find. It took me about 7 visits, I found 2, then I decided to get on a diff server and I took me 1 visit, 5 Younglings to find my (S/S).
Another good time when speed is important is if you have a pet that can do "Dodge" if he goes first it actually is 2 rounds and not 1 though it says "for 1 round". It counts for that casted round and the next, which is LAME if you are up against but good if it's you using it.
Of course (P/P) is great for pets that can heal for a nice amount. I don't know about dot heals though, if I'd be worth it. I LOVE MY EMERALD PROTO-DRAKE
If you like to pvp pet battles it is important to have the right breed, but not essential, it can be the determining factor in a loss or victory really. Get an addon so you can see what breed you have before you go around wasting gold in the AH or precious battle stones. GL and have fun =)