There really were not very many similarities at all between the Articles of Confederation and the Constitution that replaced them. The people who wrote the Constitution were so unhappy with the way things were under the Articles that they changed most things about the government.
The only truly important similarity is that both documents set up democratic systems of government. This was a truly important thing at the time because it was very different from any other form of government. Both documents explicitly went away from monarchy, which was the most prevalent system at the time.
In addition, both documents set up governments that were in some ways limited. They both set up systems in which governments were not allowed to do certain things. This was an important idea at a time when governments tended to be able to do whatever they wanted.
There were a few other similarities, like the fact that the states are not allowed to conduct foreign policy under either document. But these similarities are very minor. The only major similarity is that both documents create systems in which there are democratically elected limited governments.