I'm not sure that either function is "better" served by government though. There are many cases of very successful privately run "police" and firefighters. Generally speaking I think any function is run better by a person who has the greatest motivation to succeed. The greatest motivators in business are profit and love of the job.
Depends on the environment. In the large city where there is a need for specialized equipment and training, then you need a government entity to help finance and maintain it. If you are talking about a small town police or fire department, then volunteers would probably work fine.