To me non-profits do far more good per dollar than the government does through general taxation. The biggest reason why is that non-profits have a much more defined scope and mission.
There isn't any such case, if approached realistically. Government agencies spend trillions of dollars each year on helping the poor, the old, and the disabled in various ways. They do so in ways that are fantastically accountable (compared to the private sector), including but not limited to the fact that basically any document about anything written by anyone working at these agencies can be requested by a member of the public and the government must give them a copy. The executives working at government agencies are paid frugally, their books are audited regularly, and they are subject to dismissal for even minor transgressions.
Total charitable giving in the U.S. is an order of magnitude lower (even assuming that every cent was spent on something good, which is far from the truth), their accountability consists of (at most) a mandatory report every year and nothing else (often not even that), and their executives are now hitting 7-figure salaries.
It's not even close.
I'd say they're less accountable. There's no democratic oversight, FOIA doesn't apply to them, journalists have less incentive to go digging for dirt. They have to keep the donations coming, but that's as much a question of PR as of how much good they're actually doing.
I've no doubt there are effective NGOs and wasteful parts of government, but I suspect a large proportion of NGOs (not those on your list perhaps, but the money-weighted average) are less effective.