I don't think it's either-or. Conditional and unconditional cash transfers [1] have many of the benefits of free-market competition (focus on efficiency and cost reduction) with many of the social benefits of an expanded welfare state. I could easily see a system where people get "medical vouchers" to spend on their most pressing care problems, and providers compete to supply care at the lowest possible price to either vouchered payers, or those paying in cash.
[1] http://en.wikipedia.org/wiki/Conditional_cash_transfer
See also: http://www.economist.com/news/international/21588385-giving-...