Casa,
Red snappers do prefer deeper water but have been overfished in Belize for years because of the taste. That would be my second favorite fish (hogfish would be first).
However, a mutton snapper is nothing to scoff at...it has exquisite texture and flavor. Yellow tail, well, we ate them when we had to but not highly considered. Oh, and a mangrove snapper and grey snapper, I do believe, are one in the same.