@Stfuppercut - mentioning you I saw you wrote you'd get the Wolf for raids and that's what prompted me to write this. (You were in guest though, so I did not quote because it wouldn't notify.)
Since the dustruction of many old websites that were in my favorites the last couple years, a lot of the old math and info about hunter raid pets has disappeared. I thought I had links to some before, but if there was info in their old guides regarding it, they've all disappeared.
This is all very rough math as there are many things I don't know, can't know, or can't recall (crit chance of group members, crit modifiers for pets, focus formula), but I have tried to err on the side of caution for that. It's also very late where I am, but I wanted to simply demonstrate the possibility at this point. If there's mistakes, please point them out. I want to get to the bottom of this. The math certainly isn't perfect, and if someone has a guide with awesome math please let me know.
Re-examining it now (https://classic.wowhead.com/spell=24597/furious-howl) something is odd. 30 yard range, but it says only 15 yards within the description?
As for its DPS - (((45+57)/2)/10) = 5.1 dps per person before accounting for crit or other factors. Depending on the range that could cause problems, but I'm going to go ahead and assume all 5 people in the group get the buff and therefore it adds roughly 25.5 dps total before that other stuff.
Going to throw in that a hunter with a parked Wolf that is purely PvE will likely have https://classic.wowhead.com/spell=24295/monster-slaying , but I do not like this talent as it is a waste in PvP for the most part unless I am hitting a Druid or another Hunter's pet. Personally, I won't have it so it is irrelevant to my goals, but may not be to others'.
A quick look at Wind Serpent shows https://classic.wowhead.com/spell=25011 ... ing-breath before ZG and https://classic.wowhead.com/spell=25012 ... ing-breath after ZG (84 and 106 averages respectively).
Using the info from here it seems that it would be a 17.5% overall dps loss on bosses.
Lightning Breath has a 20 yard range, so depending on what Furious Howl's actual range is, it could be either better or worse. The Focus cost is lower however, as is the non-existent CD so even without a focus calculator I can assume it can be cast more often. How often? Remains to be seen.
84 and 106 with the 27% +damage added from https://classic.wowhead.com/spell=19620/unleashed-fury and the Innate bonuse of being a Wind Serpent (Wolf's buff isn't a damage spell so I don't think he gets bonused for it) will become 106.68 and 134.62 before losing 17.5% from boss resistance and becoming 88.011 and 111.0615. If the wind serpent regenerates enough focus to cast three Lightning Breaths in ten seconds then the gap is closed at 3 casts for Rank 5 and already surpassed for Rank 6.
Assuming 3 casts per 10 seconds (a complete guess, but it is the threshold):
88 x 3 = 264 / 10 = 26.4 dps (Rank 5)
111 x 3 = 333 / 10 = 33.3 dps (Rank 6)
I made the buffs additive for the damage multipliers in my math above as a form of rounding down because I didn't want to get artificially too high if they were the opposite method.
I do not know how pet happiness interacts with Lightning Breath, but if it gets a 25% bonus for that too that would be pretty awesome and definitely a game changer.
As a reminder, this is all before adding in 15% crit from https://classic.wowhead.com/spell=19602/ferocity or adding in the Crit chance of the players receiving Furious Howl (or armor reduction, but boss armor is thought to be possible to lower to zero so it probably won't even matter).
Additionally, on fights where the pet can melee without dying the Wind Serpent's higher innate damage modifier will also allow it to achieve higher DPS than the Wolf.
I intend to test this on Classic when I hit 60, as well as retest the cat pet, but right now it feels like the Wolf pet is looking dubious. I normally would not care to promote the idea of one pet over the other except the amount of pressure Rogues and Warriors often apply in their attempts to raise the meters for themselves just a tiny bit at the expense of overall raid dps. If Wolf is the wrong pet (as preliminary tests on Kronos showed it to be, at least for MC/BWL), we should not be pressured by urban myth to hinder ourselves and take a Wolf to raids. I won't stop anyone else that wants to take a wolf, but I want some good numbers backing me up as to why I am not.
The cat pet is a lot trickier to test as its strength relies on how many buffs you can get for it as well as what boss you're currently fighting (length, mechanics, etc.) or even what raid you're currently in (overall efficiency of fights).
EDIT: Other unknowns I just thought of are Hit chance of players and hit chance of Serpent