As a rule you lose 2 stops for a CP. For alot of people they work great and I do use one from time to time mostly on landscapes with lots of light or with a tripod in low light, or hikes in the woods. However for the most part they don't fit in with what I like to shoot (nature) because I can't afford to give up 2 F/stops. Example, during the buffalo run I needed the CP to cut the glare but I also needed to stop action for sharp images. I was shooting the 400 5.6 to get an up close perspective and with the CP I wasn't able to stop the action even on that bright day. It took a SS of 1200+ to get a sharp shot shot shooting into water with a colored bottom and dark fast moving fish at 5.6. I'm sure I could bump ISO and suffer the noise but in my experience water shots have a lot of shadow noise and that bothers me.
Same for birds and most other animals that move. I'd rather edit for color in PP and have my 2 stops in the camera while I'm shooting. Then there are the boat shots near dark... See what I mean?
Follow the link I posted and read it, its a great read.