All pets have a set statistic pool based on their level and rarity. Among each type of pet you will see variations, as you noted. Some pets will sacrifice health for a boost in attack and/or speed. Some will favor one statistic above the others. Some will demonstrate a more even spread.
Pets of equal level and the same quality all share an equal statistic pool, regardless of their individual stats. In this regard there is no "best" pet. You should instead be looking at the abilities of the other pets on your team, the attacks the pet is capable of learning, and your personal preferences. Select a pet that corresponds to your personal battle style.
For example, I was considering which of my Ravasaur Hatchlings
to train. The Hatchling generally favors its speed stat. Additionally, its type ability relies on having taken substantial damage before it activates, so having action priority is useful to get an attack in before an opponent has the opportunity to finish the weakened Hatchling off. It also learns the ability Flank, which inflicts additional damage if the Hatchling acts first in the round. I personally favor high-speed pets, so I went with the Hatchling that boasted greater Speed than than the others. Its other stats may be lower, but the other members of my team can be selected to accommodate this failing.
Wild pets tend to follow the same set of conditions, though there does seem to be more variation among wild pets of Poor, Common, and Uncommon qualities. I imagine this will be explored in some detail over the coming months but it's too early to determine what, if anything, those investigations will reveal.