The question is effectively the same :3
I would pick NIN, only because most people don't see MNK as a tank for things like Ambu, and would prefer 7 shadows over anything. Without much effort, NIN dwarfs MNK for tanking due to Yonin and damage negation, something that MNK has trouble with when using counterstance. I've seen NIN requested over MNK before, despite having superior DPS on MNK.
Also, in stuff like Dynamis, Ninja is great due to being able to walk through practically every TP move that is physical, which helps out a ton for your healers. There's still a good bit of things that shadows works on, so you get mileage there.
NIN also has a much easier time 5-stepping than MNK, IMO. They also don't rely so heavily on timers to deal the brunt of their damage, though they do so with buffs anyways. I'd go with NIN just based on where it is in relation to MNK in the community meta