CDR is a real time copy while aux copies (DASH copies) are done on a schedule. Also, CDR will make an exact replica of your disk. This means that if for some reason you had a corruption in a file on your source copy, it would get replicated to the destination copy. Aux copies will copy to another independant copy (tape or another disk library) so if you have a corruption on your source file, the aux copy will most likely fail or at the very least, shouldn't replicate the corruption over.
I think about CDR more for a DR copy where you don't want to lose any data and keep a good RPO (like MS DFS-R if you're familiar with it) while aux copies are more suited to make secondary copies of your nightly backups.
Hope this helps.