I think they probably do different things. One method sets the system so that it makes good works effective in the macro, but it probably takes the micro to actually drive the good home. Don't they compliment each other? As in, when you have a lack in either of the categories you just leave a lot of misery on the table?
Private charities do do good work. The caveats here being that the ones who are actually intended for helping the less fortunate. Many things which according to the tax code are charities do not in fact have anything to do with aiding the poor or people in trouble. And, in no small number of cases, the charities which are about aiding people fail at their mission for various reason, or are run by people who have an agenda other than simply helping people. So you get the Red Cross utterly failing in Haiti. Or church groups more focused on saving souls than bodies, and so are spending the money to influence people more than aid them.
So the hybrid model of government money and private delivery is not that good of one. There's no accountability. So my uncle runs a small town church food pantry. Half his money comes from FEMA. That works. Does it work better than just giving the poor more foodstamps? Nope. And what if the other church in the other town, the guy running the show is pocketing some of that money? Is there a reporting method by which FEMA could catch and prosecute that guy? Nope. And it is very inconvient to the recipients as well. They get less choice, and it uses a lot of their time to do it. Occasionally around here I'll drive by a church that runs a food pantry out of the back of a truck. People will stand in line for half a day to pick up the 1 or 2 bags of groceries that they are allowed. That's time they can't be spending looking for work or caring for their families.
GW Bush's faith based initiatives program was well intentioned. But not successful in practice. Now that's mostly the fault of people in Washington, not the people on the ground in cities and small towns. For all of GWB's 'compassionate conservatism', he was surrounded in office by people who's primary religious convictions were crony capitalism and international imperialism. And those are the people who set and executed most of the agenda.
But even when money did get to the faith based service groups, it wasn't necessarily well spent. The most effective, and cost effective, aid programs are usually the simplest ones. Just give people money. With as few restrictions on it as possible.
Local governments are better at providing housing, and a range of social services such as child care, education, counseling, job search. But in all of American history the only agency which has ever done a competent job of income support is the US federal government.
That's not to say that private charities don't provide good help. Every little bit counts. But they are marginal players to the problem as a whole. A week ago my mother made a mistake and cooked up a gallon of baked beans for a church dinner which was actually scheduled for this week. So I got home from work and she tells me she doesn't know what to do with it all. I looked up some stuff on the net, made some calls, and took it to a soup kitchen at a local church. 2 nights a week the place cooks a dinner for a dozen or 20 people. Now I'm sure those people need it, they're grateful, and are better off for it. And the volunteers running it are good people with the best intentions. But this is a town of 50,000 people, and more than 20 of them are poor. And even that 20 people are only getting 2 hot meals a week out of it.
We in America do a pretty piss poor job of aiding the poor amongst us. But take the federal money out of it, and what you have left, no matter how well intentioned, is a travesty.