FPS is oversaturated and will decline. I think what will happen is what is already happening. People will stick to the cream of the crop - CoD, Halo, Half-life, etc. and more and more ignore the others.
Music games offered little variety and frankly GH/Rockband were the most expensive flash games ever made. Besides, once you own one, you can just continue to download new songs, there's simply no reason to buy newer editions. But I think people have just gotten bored with them.
FPS offer much more variety and will decline slower, but as all things they'll go out of style only to return later on with a fresh coat of paint.