Really there are a few benifits. Without a doubt, looks is first. They will discolor a little with time, but never to that burned chrome look. And rusted out headers are never a concern.
Performance wise, like Ztoy said, coated headers keep heat in the tube and helps lower underhood temps. Cooler air is more dense, carries more oxygen, if the tuneup is right, the motor will make more power. One other thing,,, keeping the heat in the header tube helps the exhaust flow. Hot gasses can flow faster down the header tube, offering better cylinder scavaging. All in all, I don't know of any place (other than cost) that coated headers don't offer huge benifits over uncoated ones.