From what I've experienced so far, NIN is about 3-4% behind MNK in DPS. However, TA more than makes up for that. Math below:
TA is up for 10 of every 60 seconds, and provides a 10% boost in damage. On average this is a 1.67% boost in damage. But this is for the whole raid. Now lets assume healers arent DPSing, and that adding both tanks damage together is the equivalent of 1 dps. Thats 4 DPS that receive this boost in damage (not counting yourself, since that was already built into the numbers). 4 x 1.67% is 6.68% DPS, which nudges NIN ahead of MNK. If you time the TA with burst phases, and your healers DPS then this percent increase will be even higher.

That being said, I believe MNK brings more to the table in regards to AoE.

NIN and MNK seem to be fairly balanced, with NIN having the slight edge on single target and MNK having a slight edge in AoE fights.