I've both nin and mnk and cleared A4S. If for progressing through savage turns, NIN helps alot for raid wide utility and DPS. Shadewalker ups MT's aggro, and Smoke Screen will help your healer reducing threat when needed especially mass AoE heals. MNK has personal high DPS if you perform well, but that's it. -int would not be too important. Both is viable in your situation, but I would prefer NIN.

Another note, MNK is easy to master, its combo attack are kinda dumb-proof, meaning you will never lose a dot/debuff/buff after you learn a dungeon/raid. You will only need to learn when can you charge your chakra/use tornado kick/use purification/meditation. NIN is hard in a way that the role has a total of 5 buffs/debuffs to maintain, but since you have a war in party, you dont need to worry bout dancing edge too much bringing it down to 4 (2 dots, Huton, TA timing). I love both roles, and switch around them for raids depending on mood , hope this will help