Neither is obviously more efficient than the other overall, it depends on the structure and the incentives. People worry about private prisons for example. If you make it so the government sends people to prisons and you pay the prison a fixed rate per prisoner, of course you're gonna get skimping on services by the prisons. If you instead give the prisoner a voucher for a prison and make them pick where they go and prisons get money per voucher they get from prisoners, you're gonna get competition on quality so you'll get high quality prisons. Opposite outcomes with just a change to incentives.