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Depends what's in the rest of your list, I guess.
A Black Orc Big Boss and an Orc Warboss are essentially identical stat-wise so it comes down to their special rules.
The Warboss is tougher (a bit) because his Boss Shield works against shooting whilst the Big Boss' Tusker Shield is combat only. If taking a pair of choppas, he also does a bit better because he gets 2 bonus attacks, not 1 per 6 rolled.
Where the Big Boss excells is if he's near another ORRUK HERO to show off to.
The Warboss is better as your general (Waaaggh! is an awesome command ability, whereas the Big Boss only helps IRONJAW units that shouldn't be having problems with Battleshock anyway)., whereas the Big Boss is better as a bodyguard - take the shield, stay sheltered behind a unit, move out and charge someone trying to get at your general or TOTEM - and the orc you're protecting will grant you bonuses to hit into the bargain.
The Tyrant is a bit tougher and better in a fight, but it's pretty much a wash compared to a Boss on a Boar. The main difference, again, is command abilities. If you have ORRUK units, you want the Warboss. OGOR units, the Tyrant.
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