There are many differences between these two types of additional Medicare coverage. Medicare Supplement Plans, or Medigap, are designed to pay the out-of-pocket costs not paid by Medicare itself. These plans don't include prescription drugs, tend to have higher premiums than Advantage coverage, and you'll pay more if you don't enroll early on in your Medicare coverage. On the other hand, Medicare Advantage Plans are usually much lower in premiums and higher in out-of-pocket costs. Advantage policies often have prescription drug benefits. But, Medicare Advantage doesn't pay any of the costs that original Medicare doesn't cover. You can't be enrolled in both a Medigap plan and an Advantage plan at the same time.