No.
Gear isn’t spec specific.
Fury prot generates more threat baseline. Fury prot generates more threat in the same exact gear as deep prot. Both specs can gear for mitigation or for threat.
There isn’t 10%-30% more mitigation in a deep prot build. Both specs can and do use a shield. Fury prot doesn’t need world buffs to make Enrage, Flurry, Deathwish, and Bloodthirst stronger threat tools than 1h weapon mastery, Impale, and Shield Slam.
Shield Slam does 350+block value damage +250 flat threat. Using Elementium Reinforced car door, that’s 54+19 = 73 block value. Assuming you’re gearing for block value, which at this point in the game is Wrath Boots, Wrath Shoulders, and Styleens for 14+27+24 = 65 more block value. This brings your Shield Slam damage up to 350+138 damage + 250 flat threat for a total of 738 threat, at best.
That means that BT needs to hit for more than 738 damage to beat SS flat out in threat generation, which it does. BT matches that damage at 1640 AP. BT easily hits for more than 738 damage with just raid buffs and consumes; hell, it hits for more than that when just running a 5m dungeon or solo farming with Deathwish or Enrage procs. What you’re also ignoring is the additional white damage and additional HS threat from Flurry. On top of that, you’re ignoring Deathwish, which is 20% more threat for 30s. Lastly, you’re ignoring Enrage, which increases all threat by another 25%.
By the way, this is just comparing fury prot with a shield on to deep prot. Once the spec uses DW, the Flurry up time goes up, the Enrage up time goes up, and the rage generation goes up. From the extra attack speed of Flurry and rage generation, Fury Prot uses double the amount of HS as deep prot. Even when both specs are under infinite rage conditions, Fury Prot will use 25% more HS with the same weapon due to Flurry uptime.
At no point in the comparison does Deep Prot ever shine for threat generation. The spec is completely blown away by Fury Prot and offers only utility for trash pulls and flat threat for fresh 60 tanks with no raid gear whatsoever.