The stiffest, most bone jarring bike I ever had was steel and the whippiest wet noodle I ever had was also steel. I had 1 aluminum road bike (CAAD 5) and it was quite harsh. I have a titanium Seven now and it is close to the CAAD 5 but I have ridden a Moots and it was like a spring compared to my Seven.
The only cf bike I've had is my mountain bike but I don't think you can say a certain material will always ride a certain way. As others have said there are other factors beside material.
Other factors are rider weight and road surface. If you're on a smooth road anything will work. I don't believe a little bottom bracket flex is going to matter to most of us. A bike that's too stiff will beat up a light rider more than a heavier one, however.