I recently got rid of my French Angel. It was getting large and aggressive. My Moorish Idol, who is now almost 4 1/2 years in my tank, was losing weight because the French was eating food before the Idol could get his fill, and because it was chasing the Idol a good bit. I decided that the Idol's health was more important than having the French Angel, and got rid of it.
The big problem with the food is that the French would gobble all the food up and there was none left for the Idol to graze on. Idols don't eat a lot all at once, but eat all day long. I feed a lot of pellets, some get eaten right away by most the fish, including the Idol. But the rest sit on the bottom and get consumed throughout the day, until I feed again at night where the process repeats itself. The French ate everything quickly and left nothing to graze on. So the Idol was losing weight and it got where I began to see its ribs.
Also, I had not fed Nori for quite some time. I have found that the streamer does not grow unless the Idol has some greens to eat, be it algae or Nori. Result, it's streamer was short and didn't grow.
Here is the Idol when the French was with it, and I had not been feeding Nori. Ribs were visible, and streamer was short.
Here it is a few weeks later, no French and being fed Nori. Much fatter, can't see its ribs, and much longer streamer.
Color is a little paler in the second shot because it is late and he is somewhat changed into his night time colors.
In short, in my experience, I have found that the Moorish Idol needs to eat greens, and needs some amount of peace, and needs to feed all day to do well.