Since PvP is a far more fluid type of battle, where even the same opponent never fights the same way twice for the most part, you need to think far more carefully about what breed of pet you want. Some of this is dictated by what moves your pet has: a hard hitting move benefits most from power, for example, so having a pet with high power makes the best use of such a move. If you have a pet with a high percentage healing ability, having it with higher health means that, not only does the pet last longer, but when you do heal, you heal for more.
There are other things to consider as well. Undead, for example, are often preferred with high health because they last longer, and since they’re very slow anyway they’re most often going second. Since this is what people expect however, having an Undead with decent speed can make a reasonable difference to a fight.
It often pays to have multiple breeds of the same type of pet for PvP, as it allows you to switch out pets based on what sort of play is happening that day. It also gives room for you to experiment with what sort of teams work best for you.