Not always true. I tried COD on the PC a couple times and was playing just as good as I was on 360. It's just a matter of getting used to keyboard and mouse. If all platforms were allowed to use their respective controllers, I think it'd be a good match.
I'm sure it's not always true but theoretically the mouse and keyboard are more effective in every way. I, however, prefer the fluidity and controls of console; it feels less like 'button-pressing' and more like timing and movement of the controls. I guess I prefer the more tactile feedback.