For areas where occasional failure and/or occasional required provider changes are tolerable (basic education, for example, may not qualify as one of these):

competitive market > govt control > uncompetitive market

to be more realistic, there's overlap at the ends of these - you can find some local govts that outperformed competitive markets and some uncompetitive markets that outperform local govts, but on average, the above generalization works.

The real pain is that all the incentives that make capitalism work well ALSO incentivize finding ways to break the market, so a competitive market won't stay competitive forever just by existing.