Mix of the two works best a la Australia + Most of Europe.

This means that the government/government business enterprises (GBE's) handle the key infrastructure and the provision of public goods (water, electricity, public healthcare as a safety net for those that can't afford private, transfer payments), and then private businesses handle the provision of consumer goods.

Obviously a complete totalitarian nanny state isn;t really ever a good thing, welfare or not. But the governing bodies ensuring a minimum standard of living for it's citizens? That should be one of their primary responsibilities, entailing welfare payments, provision of minimum standard of healthcare, etc etc.