I use 1/2 inch with 3/4 outer hose.
If you use, or intend to use a pump, particularly the March that everyone uses, don't use 3/8. Too much internal resistance, so very Very low flow.
If you intend to keep using gravity then, yes, 3/8 has better surface area to volume BUT:
Assuming you intend to use a single pass through your CFC to your fermenter, and if you are going to brew lagers, especially all-grain, then you will be leaving most of your wort at high termperature for too long and forming DMS.
Use a CFC if you are going to use a pump, and recirculate back to your boil kettle, therfore dropping all of your wort temp at the same time, before then diverting to your fermenter. Therefore use 1/2. Additional benefit of being able to whirlpool, and avoid taking break and hop to your fermenter.
Otherwise, use an IC.