The threat modifiers for Bear tanks are the same as Warriors: 130% for Bear Form and Defensive Stance, or 149.5% if you have 5/5 Defiance or Feral Instinct. However, the primary bear tanking abilities dont add threat like warriors', they multiply. Each point of damage done by Maul and Swipe does an additional 0.75 threat, before the bear stance modifier. E.g. Maul does 200 damage, so it does 200 * 1.75 = 350 threat raw, or 350 * 1.3 * 1.15 = 523 threat counting the bear stance + feral instinct modifiers.
It should be pretty trivial to calculate an approximate TPS for Bear tank, since they only really have two abilities for generating threat: Maul and Swipe.
Maul rank 7 (which is what you have at level 60) adds 153-154 dmg to your "next attack" (same mechanic as heroic strike), but for every point of damage it has a threat multiplier of +75%.
Swipe rank 5 does 99-100 dmg every GCD(1.5 secs) and has the same +75% threat modifier to the dmg it does.
Natural weapons 5/5 increases all dmg done by 10%.
So Maul becomes 168.3-169.4 dmg (168.8 avg)
Swipe becomes 108.9-110 dmg (119.5 avg)
Now, I have pretty much BiS pre-raid bear mitigation gear (so for a fair comparison, the warriors would have to be in the same level of gear, everyone can gear differently for more threat and less surival ofc), so I'm just going to go by my base stats, add raidbuffs and then attempt to calculate the average TPS.
Unbuffed stats of relevance to threat:
108 str
178 agi
21.8% crit
dmg: 219-280 every 2.5 seconds, for a total dps of 109.9
Unbuffed TPS:
Average hit is 249.5 (5/5 NW included), plus dmg from maul 249.5+168.8 = 418.3 dmg
Including 21.8 % crit that's an average hit of 509,5 every 2.5 seconds from maul.
Maul does 75% more threat than just white hits, so total TPS from maul is with bear modifier and feral instinct it becomes
509.5 * 1.75 * 1.3 * 1.15 / 2.5 = 533.2 TPS from maul
Swipe is super simple, it's just
119.5 * 1.218 (the crit %) * 1.75 * 1.3 * 1.15 / 1.5 = 253.9 TPS from swipe
So unbuffed bearform, assuming infinite rage generates a TPS of 807 (on a target with no armor ofc).
To make this more realistic one should add the dmg reduction from armor of the target, and the total avoidance of the target (chance to be missed, chance to dodge and chance to parry incoming attacks). I don't remember these numbers so I'm just going to make them up, it should not make a difference if you make a comparison if you just apply the same numbers for a warrior tank as I use here.
Putting dodge, miss and parry at 5% each means a total avoidance of 15%, then add another 20% dmg reduction from armor it's 807 * 0.8 * 0.85 = 548.8 TPS.
If we add raidbuffs, that's another 16 str and agi from imp MOTW, +290 AP from Imp BS, 222 AP from Imp Blessing of might (whether anyone have these buffs improved is not important, just make sure the are applied consistently in comparisons), BoK increases all stats by 10%.
108+16 str * 1.1 = 136.4 str (136.4-108= 28.4 more str, which is 56.8 more AP from BoK)
178+16 agi * 1.1 = 213.4 agi (213.4-178= 35 more agi, which is +1.5% crit from BoK, for a total crit of 23.3%)
290+222+56.8 = 568.8 AP from raidbuffs. Since you get 1 dps for every 3.5 AP this would give an additional 162.5 dps.
Adding critchance and 5/5 NW that's 162.5 * 1.233 * 1.1 = 220.4 dps.
Reduce this by avoidance and armor of boss: 220.4 * 0.8 * 0.85 = 149.9 dps.
Adding bear modifiers and maul: 149.8 * 1.75 * 1.3 * 1.15 = 392.1 extra TPS from raidbuffs.
For a total raibuffed bear TPS of 548.8+392.1+(1.5 * 253.9 * 0.8 * 0.85 (recalculating swipe TPS with +1.5% crit)) = 1199.9 total raidbuffed, pre-raid BiS Bear TPS.
Yes, you read that right. Since the bear modifiers are multiplicative, and bear threat comes primarily from maul dmg, the bear TPS scales enormously well with raidbuffs (and better gear, since higher level leathers basically just add more agility, str and sometimes even crit and hit).
That's pre-raid BiS gear. That means, if your DPS has salvation buff and no other threat modifier, they can pull
X * 0.7 = 1199.9 <=> 1199.9/0.7 = 1714 dps before they pull aggro.
This is all idealised of course, in-game there will be periods of chained crits for amazing TPS, long periods of avoided attacks for super shitty TPS, rage starvation periods etc. etc. that affect all tanks. I'm not familiar with the threat caused by warrior attacks or their cooldowns, nor their unbuffed pre-raid BiS stats, so someone else has to do the warrior calculation.
Tanking time is not that long - Frenzied Regeneration helps too, sometimes
