I like PPs best.
Pure health breeds mostly only have a bit more health, not enough for a big hit, only mediocre at best. Getting more health just ensures you - might - last one round more. Speed is a funny stat, either its wasted points if you want to go 2nd or good if you want to go first but you will need just 1 more speed stat than your opponent, any more speed is wasted aswell. It just seems power is the most reliable stat, you can't get enough of it. Also looking at damage/accuracy ratios, with more power you could get more reliable attacks. Not that theres many cases, but in theory.
But in any case, moveset+racial, tweak the possible breed to the pet, individual judgement.
Pocket Reaver and Personal World Destroyer has almost same moveset. PWD is singlebreed HP, the Pocket Reaver can reach 341ATK as PP, quite powerful with the Supercharge and a Metal Fist to the face. If I chose Pocket Reaver HP I'll get a copy of the PWD, what use is that?
That's why I hate and love breeds, such a time consumption but when done right, quite powerful pets can emerge.
In a PvE aspect you will know your opponents speed and can tweak the speed on your pet accordingly and get the stats used in either health or power and still be fastest/slowest depending on what you want. In PvP aspect you have a hunch of whats popular to use right now but you can't know for certain what you're going to meet, what breeds they have. Everyone wants to go first in PvP to control the fight so people stack speed like madmen and hope they have the highest speed stat.