The limitation I see with using CoC is its applicability to non-Western fandoms, particularly animanga, where, yes, from a Western perspective a character is "of color", but as a member of one's own dominant group, it's a little different from tagging, say, a Sherman Alexie-fanfic.

I think that's a really good way of putting it.

Also, I don't think it's an either/or situation with the CoC tag--using both is certainly possible. ETA: When applicable.