I did some research on what people are saying is the best hunter pet in Pandaria. While I agree with those who say for raids you need something that provides buffs missing for the group, i.e. complimentary abilities; I feel majority of the commentators are wrong when they say either pet is good for leveling/soloing. Others suggest Shale Spider as a slightly better pet because of 5% buff to the major hunter's stat - Agility.
Small note on a side: I do a lot of soloing and in Pandaria, except in extreme soloing cases, you'd do just fine with ferocity pet, no need for tenacity pet.
So I decided to use Zehera's Hunter DPS Analyzer to check some numbers against these theories. I loaded my build from the armory and calculated DPS with different pets.
Generic Ferocity Pet (no buffs):
Cats used to be hunter's favorites in Cataclysm, providing the highest DPS boost when soloing and decent buff for groups too. Now, with mastery buff, they are not as good as, say, Shale Spiders.
Ferocity Shale Spider:
As expected Shale Spider's buff of 5% Agility fetches slightly better DPS than a cat. Note this option is only available to Beast Mastery hunters.
Then I decided to check out Quilen as a pet. Quilen "Bacbka" is my recent favorite for LFR because of its Eternal Guardian battle rez ability. It also provides 5% crit buff which, to my surprise, turned out to be better option than 5% Agility provided by shale spider.
I understand simulation has its limitation and crunched numbers do not necessarily translate into real-world DPS increase. However I did this exercise for two reasons. First, I wanted to see what I am missing in raids in personal DPS when using Quilen as a pet compared to other options. Second, I observed better DPS with Quilen in LFR and wanted to see if simulation agrees with that. Turned out to be for my particular build and case Quilen is the best choice.