We compare health care spending in public and private Medicare using newly available claims data from Medicare Advantage (MA) insurers. MA insurer revenues are 30 percent higher than their health care spending. Adjusting for enrollee mix, health care spending per enrollee in MA is 9 to 30 percent lower than in Traditional Medicare (TM), depending on the way we define "comparable" enrollees. Spending differences primarily reflect differences in health care utilization, with similar reductions for "high-value" and "low-value" care, rather than health care prices. We present evidence consistent with MA plans encouraging substitution to less expensive care and engaging in utilization management.