A study by the Center on Budget and Policy Priorities (CBPP) claims that Medicaid and SCHIP deliver the same care at a lower cost than private insurance (the study ignored marketing and enrollment costs). Policy conclusion: Enrolling low-income families in government programs is cheaper and better for all concerned than enrollment in private plans.
As an aside, I've never heard anyone, anywhere say he would rather be in Medicaid than private insurance. People who say "Medicaid is better" always mean "for someone else." There are also other reasons to be highly skeptical, even without carefully examining how the study was done.