In the case of an implant coated with antibiotics, I would guess that the FDA would designate the product as a device because its primary mode of action would be as an implant, not as a antibiotic. The reason being that the primary therapeutic aspect of this product would be to serve as an implant. It would be up to the FDA’s Office of Combination products to designate any device where the primary mode of action is not certain. If the the FDA does end up classifying this product as a device it would fall under the regulation of CDRH.
In the example of the drug delivery system I would guess that the FDA would designate that as a drug because it primary therapeutic function is the release of the drug. If classified as a drug then the drug would fall under the regulation of CDER.