What kind of cable box do you have? The model number will usually be printed on the front of the box somewhere.
Also, how do you have it hooked up to your TV?
Does the CC also look different on Starz? Different font/color/size? Or it just the speed thats different? I ask because I think what your seeing is the difference between the TV's CC decoder and the cable box's CC recorder. A work around if your using HDMI is to use component instead.