Nitrox has advantages over air. The decreased nitrogen in the mix means you have reduced nitrogen loading. That means that you can stay at depth longer without reaching your no decompression limits. Also, it shortens the surface interval you need between dives.
However, you increase your exposure to oxygen. Oxygen is toxic at high levels and can cause convulsions (something to be avoided whilst scuba diving). So you have to watch your oxygen levels and your nitrogen levels whilst diving. Functionally, this is not a big factor if you do not push the depth limits whilst diving on nitrox.
The problem is that diving on nitrox does not increase your gas supply. If you are an air hog and use up your gas quickly, you probably do not get anywhere near your no dec limits on air. So why bother with nitrox?
Another drawback with nitrox is that it costs more for a fill than air.
Some poeple claim that diving on nitrox makes them feel much better than they would after diving on air. I suppose that nitrogen loading could have a significant effect. But I have never heard of anyone doing a double blind study on this one. Given the fact that the placebo effect is quite large on drugs, I would think that the claims for any benefits of nitrox in this regard would be a placebo effect.
So if you are making repeititive dives and nitrogen loading would be a problem in diving with air, nitrox can give you enough of a reduction of nitrogen loading to make a meaningful difference. I believe that most live aboards (where many dives in one day is common) offer nitrox.
If you are an air hog or you are diving only a couple of dives in the day and not pushing your nitrogen limits, diving on nitrox really is not that much of an advantage.