How did the Constitution succeed where the Articles of Confederation failed?
The Constitution succeeded where the Articles failed in its rebalance of power between the federal government and the states. The states had too much power under the articles making the very necessary federal government almost a figurehead.
In addition The Constitution provides ways to solve governmental disputes, but the Articles did not. This was learned by early America the hard way and is why the Judicial Branch and the checks and balances were so carefully crafted in the Constitution.
Lastly, I think (and this just my opinion) the the Constitution was written as a document to serve a nation over time: to allow the nation to become strong and maintain its power and legitimacy with its people. The Articles were created to bind together a group of very separate entities during a time of war. This does not require a lot of forward thinking. I think the framers learned that and looked at writing the Constitution as a completely different task than creating the Articles.
The Articles of Confederation failed because they did not give Congress and the national government enough power. The new United States just fought a war to end what they considered tyrannical rule of a strong government that overpowered local government and the leaders of the U.S. feared a powerful central government. Because of this, they did not give the central government the power it needed to rule effectively. It did not give Congress the power to tax, so the government ended up printing money which caused inflation. It did not give Congress the power to draft troops, so the U.S. military was small leaving the U.S. weak. Congress did not have the power to control interstate commerce or stop states from printing their own money, causing economic chaos within the U.S. The Articles did not give Congress the power to place tariffs on foreign goods, hurting American businesses that could not compete with cheaper British goods. The U.S. government had no chief executive so there was no one to enforce the laws that were passed. The list can go on. With the rebellion led by Daniel Shays in Massachusetts, the leaders of the U.S. realized the Articles were not working which led to the Constitutional Convention where the Articles were abandoned and the new U.S. Constitution was written.
The new Constitution addressed many of the problems created by the Articles by creating a federal system of government with a much more powerful national government. It gave the national government the power to tax, draft troops, control interstate commerce, etc. It also created an executive branch and a federal court system, both of which were lacking under the Articles of Confederation. The greatest argument against the new Constitution was that it gave the national government too much power. This argument was addressed by the framers by creating a system of checks and balances, creating a system with three branches, each with its own separate powers (separation of powers), and creating a federal system where powers were divided between the federal government and state governments, with some powers delegated to the federal government, some reserved to the states and some shared by both.
The Constitution succeeded where the Articles of Confederation for one major reason -- it created a government that was acceptable to those with the real power in early America.
The Articles failed because they were not able to create a government under which there could be a "good business climate." The lack of a national government and the excess (to the elites) of democracy in the states meant that people who owned businesses could not feel secure and could not trade well with other states. This meant they could not make much money. It also meant that the economy of the nation suffered.
The Constitution increased the power of the national government and allowed for free trade between states. It specifically protected property and the rich in a number of ways. By doing these things, it created a more stable climate for business. This allowed the elites to be happy and allowed the economy to improve. That is why the Constitution succeeded.
I would say that the Constitution succeeded in the mere Preamble. The Articles were a "loose confederation of states" whereby state autonomy proved to be more important than effective governance. The opening goal of the Preamble that calls for a "more perfect union" speaks to this in ensuring that individual and local freedom does not at the cost of a government that works towards the ability to work for the benefit of its people. The Constitution worked out a system where those who were in favor of the AntiFederalist position of individual rights and local autonomy were appeased as well as the Federalist position of effective government on a national scale were pleased. In this light, both groups' worst fears were allayed. The fear of King George eviscerating rights and liberties along with the lawlessness of Shays' Rebellion were both addressed, making the Constitution a document that succeeded where the Articles failed.