They mention the events of Here Lies the Abyss if you do that first. But no major plot differences.
I prefer doing Wicked Eyes Wicked Hearts first because it makes more sense in a storyline context.
1. In order to get a massive army to Adamant, it seems logical that you would need safe passage through Orlais first. So solving the issue with the nobles is the best course of action.
2. Saving Celene seems to be the most important thing to do. The ball logically has a set date (in-universe, not in-game). So making sure you have influence to get to that ball on time makes the game seem better.
3. Influence. If you do Adamant first, then I see no reason why the Orlesian court would not automatically favor you. It makes more sense to go in with the minimum amount of accomplishments in order to justify the suspicion and condescending attitude of the court.
4. If you stop the demon army first, then who rules Orlais is of no consequence. It may as well be Abernache in this case. So securing Orlais' stability first is more sensible in making WEWH matter to the plot.
5. It would logically take Hawke some time to get to Skyhold, then Crestwood, then Skyhold, then the Western Approach. This is all time you don't have to waste in getting to the ball. Plus, this means the Warden plot can wait.
6. It's the surest lead to Corypheus' next plot. Hawke's plot is just supposition. The plot against Celene is a sure bet, and the prior quest in Redcliffe or Therinfall leads directly into WEWH.