I've eaten at both, including several times at One Sixty Blue.
Both places have been spectacular on every occasion, probably the very best dinners I've had in the city other than at the fancy "dress up" places (and this is high praise indeed). Based on the dinners I've had, I would be hard pressed to say that either is better than the other. Both have "to die for" food, and impeccable service.
Here's what I would recommend:
If you've never been to One Sixty Blue, go there. Just because it's been around longer, and more people are familiar with it if you like to compare notes with others.
If you've already been to One Sixty Blue, but not to Aigre Doux, go to Aigre Doux.
If you've been to both, go to the one you've been more eager to return to.
Don't agonize over your decision, as they are both excellent places. Wherever you choose, go, and enjoy your meal.