Radio has shitter quality than your CD's? You must have a dodgy headunit then.
My radio has the same quality of the CD's and vice-a-versa. The signal goes through the same EQ's/ speakers/ amps etc... i can't figure out why yours is bad?
Do you have a seperate radio from your CD player? Or is it all-in-one? If it's all-in-one there shouldn't be any problem with sound quality...