I was curious enough to do a test on that with a friend, since that's the next best thing to simcraft charts. We took a (roughly) max-TPS specced Bear and Blood DK to Patchwerk 10 man for a threat race, with a Holy Pally keeping us up.
The DK provided 20% melee haste, 10% AP, and Horn of Winter, whereas the Bear provided MotW, Mangle for himself, and 5% melee crit. The Holy Pally Gbom'd both of them, and the 8% Kings drums were used.
Overall, the main things we were missing were:
1) 20% Armor Reduction, Savage Combat, Curse of Elements, Sanctified Retribution, Heart of the Crusader. The former two amount to something like 12-13% more physical damage, so between those two and Curse of Ele both tanks have their damage reduced across the board by almost 13%. Technically Bear threat is reduced slightly less by this due to Lacerate's bleed not needing the Armor reduction buff, and due to how some of their inherent bonus threat amounts work.
2) 3% minor Haste, and BL, the loss of which hurt the Bear more due to how Maul works.
3) 5% spell crit, 5% spell crit debuff, 3% spell hit chance, and Crypt Fever, the loss of which hurt the DK more, even if he had 5/5 Killing Machine.
So in terms of the buffs we missed, the DK was set back more, but not nearly by any kind of significant margin. And the results were more or less in line with what you'd expect. The DK established an early and really high threat lead initially, but the Bear would catch up over time (this took about 1 min 30 seconds) and finish either right on par with the DK, or with slightly more threat than him. This happened both times we did the threat race. Each race lasted 6 mins, because that's when the enrage killed us.
Some other notes:
- The Bear wasn't using Demo Roar so as to take more damage and maximize his rage income, which resulted in saving 1 gcd every 30 or so seconds and being able to use it for threat.
- The DK was using Hysteria on himself since it was a threat race, something which he wouldn't have done in an actual raid.
- The DK's rotation was executed with maximizing threat in mind, so he used the absolute bare minimum amount of Death Strikes.
- The bear was specced 3/3 Improved Mangle and had Mangle glyphed, things he likely wouldn't have in a raid.
- The boss' 0.9 swing speed, as well as the lack of the 20% dodge debuff, meant that Rune Strike had significantly higher availability uptime for the DK than it would on something like LoD.
Bringing all this back to the point about Warrior off-tanks and Safeguard usage, it stands to reason that you should continue to be mindful of threat as a potential issue even if you're a DK tank. Ultimately, even an Unholy or Frost tank isn't invincible to threat ever presenting an issue if he's spammed with -10% threat reduction every reaper.