Medigap plans were introduced a few years after the passage of Medicare in the sixties, and offer excellent coverage. The details of what the plans cover are determined by congress, and insurance companies simply set their premiums. There is no difference between a Plan G from one company to the next, except in the premium cost. Insurance companies typically refer to Medigap plans as Medicare Supplement plans. A Medigap plan will be accepted anywhere in the country by any doctor who accepts Medicare.
Medicare Advantage was introduced under George W Bush at the behest of the insurance lobby. Medicare Advantage is seen by many as the first step in an effort to privatize Medicare. With Medicare Advantage the insurance companies can decide what they want to cover, and they can change the plans every year, so something that might be covered when you first join might be dropped a year later. You have to sign up or renew every year, and you are limited to a specific network of doctors in a particular geographical region. The plans tend to be a little cheaper than Medigap plans but over time as you get older they can become increasingly expensive.
Here is an excellent video of Thom Hartmann explaining the Medicare Advantage scam:
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