Social insurance programs are sometimes centralized, with all design and policy decisions made at the national level, and sometimes decentralized, with some level of local autonomy. In this paper, we study the trade-offs involved with decentralization of administration of social insurance programs in the context of social health insurance programs in the U.S. by comparing the two largest health insurance programs in the country: the Medicare program and the Medicaid program. We first use a novel identification strategy where we follow Supplemental Security Income (SSI) beneficiaries as they exogenously transition from Medicaid to Medicare at age 65 to estimate causal differences in spending and outcomes for the two programs. We find that it costs about 30% more to insure an SSI beneficiary via Medicare versus Medicaid, but that Medicare also produces better outcomes. We then assess causal differences across state Medicaid programs using a border discontinuity strategy where we compare health care spending and health outcomes for SSI beneficiaries living in the same small geographic region but on opposite sides of a state border, using SSDI beneficiaries enrolled in the Medicare program as a control group to capture any residual geographic differences in health at the border. We use these estimates to assess whether differences across state Medicaid programs reflect differences in program efficiency versus state preferences for trading off spending and health.