Battle Pet BreedID is a standalone addon that will display the Breed of any pet in the following situations:

In Battle
In your Pet Journal's scroll list
In your Pet Journal's pet description tooltips
In Item tooltips
In Chat Link tooltips
In the "Collected ..." line (with BattlePetCount installed)

Theorycrafting is up to you... but if you know what stats you value most, now you can find them! To learn how the Breed ID affects your pets, go here: http://www.warcraftpets.com/wow-pet-battles/breeds/.

This addon uses the letter system by default (B/B for breed ID 3, etc), but if you want to switch to the number system used by other resources, just type "/breedid" or go to Interface->AddOns to open the Battle Pet BreedID options panel. You can change the format type at the top in the Dropdown box, along with over 20 other different options!

Notes on special breed results:

If a pet's breed displays as "NEW", no base stat data is available for the pet yet. This usually only happens for pets introduced suddenly (like Blizzard Store pets or encrypted Holiday pets). I'll likely post a new update soon resolving the issue, as I am continually updating the addon with new base stat and breed data.
If a pet's breed displays as "ERR" (or something similar), a bug has occurred. Please report the circumstances in the comments on CurseForge, and I'll try to resolve the issue (which is likely to be related to other addons).
If a pet's breed displays as "???", this is not a bug. This addon works by taking the pet's raw stats (species, level, quality, health, power, and speed) and doing math to determine the breed based on known base stats (supplied by the addon). However, in some cases, 2 breeds can have identical health, power, and speed values while the pet is at level 1 (well, they really aren't identical under the hood, but because of rounding the decimal values, they appear identical to players and the API). The best way to solve this is to increase the level of the "???" pet to level 2. No conflicts exist past level 1, so it will resolve into the correct breed.