How do the Article of Confederation compare with the Constitution, esp. regarding specific powers given or denied the central government under each?
The Confederation Government was formed with the intent and purpose of retaining the sovereignty of the individual states, as is stated in its opening language. There was a single House of Congress with no Presidency of the United States and no judiciary. The Confederation had jurisdiction over foreign affairs and the unorganized territories of the U.S.; but not much else. There was no power to tax or regulate commerce between the states; a two thirds vote of the states was required to pass legislation and unanimous consent was required to amend them. They were, in fact, never amended. The system created was cumbersome and unworkable and understandably did not last long.
The Constitution arose from a convention called to "Amend" the Articles of Confederation. It soon decided they were unworkable and were abrogated. The Constitution grants eighteen specific powers to Congress under Article I Section Eight, including but not limited to the power to tax, the power to regulate commerce among the several states, declare war, coin money, issue patents, etc. It also grants Congress any power necessary and proper to carry out the enumerated powers. It's limitations are that Congress may not pass ex post facto laws or Bills of Attainder, or grant powers of nobility. By Amendment, the rights listed in the Bill of Rights are protected. Finally, the 10th Amendment states all powers not prohibited to the states are given to the Federal Government are reserved to the states. The latter amendment is a favorite of Tea Party supporters.