Your other tank you didn't have trouble keeping aggro from after taunting might be a warrior. They lose access to one of their hard-hitting abilities (Revenge) when not being actively hit, as well as not having rage generation to do much more than Devastate and Shield Slam. In fact, warriors are the only tank that is so completely hamstrung when not being hit, since they can't use Revenge and rarely will have the rage for Heroic Strike as well as losing their vengeance stacks.

If you taunt from a bear or DK, and you have no vengeance, that 60k+ Mangle or Death Strike they hit next can put them pretty far ahead in threat. Sometimes on my bear I even have to stop auto-attacking for a few seconds. It's not such a big deal if there's a couple minutes of threat built up, but taunting for that first Impale on Madness, or that first or second tank swap on Ragnaros, if the other tank doesn't stop attacking for a bit they'll probably pull aggro.

Also, on H Alysrazor, our tanks even stood in Alysrazor's firestorm to try to keep their vengeance stacks, but I think they said it didn't work. They had to swap in a few dps pieces to lower their avoidance so they could stack vengeance fast enough to kill the birds.