They have their own separate set of obstacles based on the definition of what they are. Then you're posing a loaded question. What kind of government?
How is Blackwater, a paramilitary organization, operating well alongside our military. A military which by your definition is in direct competition with Blackwater?
There is a level of synergy that is trying to be created between both concepts but you feel to only see it as black and white. The surface tension is essentially "I'm not paying tax money so some poor nigger can have crack babies aborted." This may not be your frame of mind, but that's the sort of fear being played on by plucking those delicate strings of the base of opposition and you're being sucked right into it.
So in your tin-foil hat world yes the government has an innate advantage because Hilterbama will exterminate the whites through death camps because it will use the military and propaganda to enslave the citizenry.... oh wait wasn't that something
Bush and his neo-con advisors tried to do?
In reality, in this specific situation, no the government does not have an innate advantage over a private for profit entity. If anything, in our current government, a private entity has the advantage as we see with astounding statistics like 374 lobbyists per congressperson.
A government-backed program has no financial influence and is subject to the ebb and flow of politics. As soon as a republican majority comes back it will be watered down all to hell or removed completely. So please, stop with the naive babe in the woods act and get with it, man.