I can almost 100% guarantee that the current savage tier will break TBN with 2 autos. I'm taking a break from this tier so I can't give boss auto numbers, but Titan last tier autoed for 33k and TBN shielded for 38k at the time, so the same logically should hold true now. As for commenting on Equilibrium in particular, it's a weird skill; just because the variance for how much it can heal for is so huge. Popped alone and non-crit, 30k. Crit with ToB, like 62k. So it not critting is just depressing. As for what's better, I don't think it's a completely straightforward topic. For one thing, comparing TBN against NF, ToB, & Equil all combined just seems more than a little bit of an unfair matchup. Strong as any cooldown may be, it's bound to lose out when put in a competition against three all together, and that's another reason I think it's only proper to pit TBN against NF individually.
I will concede the point about both WAR and DRK having to lose some optimal DPS in order to get multiple uses of each of their respective CDs (or in WAR's case, multiple powerful uses). Although, on that point it should be noted that WAR does lose out slightly worse in that regard if we're comparing the loss 1:1, as DRK loses a 500p Edge under raid buffs while WAR loses a 920p IC under the same, which is a fairly significant potency difference. Now, I've never analyzed DRK's damage profile in detail so I can't say anything on that regard, but I have for WAR and Inner Chaos makes up around 17%-20% of WAR's total damage output over a fight.