Among all of these, only Bloodbeak
and Axebeak Hatchling
can deal the highest damage possible and heal themselves for a maximum value (= P/P).
Saying that, you can also pick up an H/P too if you see that you tend to overkill. Nothing disallows you to get each of the samples as these three are the same stat-wise.
If you're not sure what these abbreviations mean, see the classic guide
prepared for this website.
While flying pets are pretty flexible when it comes to breeds, remember the general rule that more hybrid breed means a lesser global bonus.