NATO certainly has a lot of value, even now when the Evil Empire has gone away. It provides a good umbrella organization to coordinate activities and provide unified command and control.
The UN has done a lot of useful work, particularly in the area of refugees, world health, etc. However, the political aspect is sometimes (usually) farcical. The Security Council is generally a long-winded talking shop because all the earnest and strongly worded resolutions are generally ignored unless some member state is willing to step up and provide the power needed to enforce them. And, of course, who does everyone automatically expect to step up and provide said power. A perfect example is the Balkans in the mid-90's, where all the resolutions and blue-helmeted UN peacekeepers were meaningless until the U.S. got involved (e.g., the Dayton agreements). A counter-example is Darfur, where the UN has essentially been impotent to stop the mass murder by the Sudanese. Maybe that's not the way it's supposed to be, but that's the way it is.