For all their sturm and drang directed at the Northern States and the federal government, the Confederacy didn't find the structure of the United States itself, vis a vis the Constitution, to be worthless and corrupt. Indeed the Confederate Constitution is, in many ways, a copy of the original American one, though with considerable nuances, adjustments and conditions built into it.
In my personal experience, most people's perceptions of the Confederacy's priorities in differentiating itself are split into two camps; those who feel the Confederacy sought to entrench slavery, and those who feel the Confederacy championed the sovereignty of the state. The Confederate Constitution reveals some truth to both views.
- The Preamble. The Preamble serves to make a sort of thesis statement for the two Constitutions. It makes it clear that this body of work intends to speak of behalf of all the people, and establishes the basic intents and concerns which drove them to create it (e.g. establishing justice and ensuring domestic tranquility, points which are mentioned in both Constitutions)
- Branches of the Government: Both Constitutions established an Executive, Legislative and Judicial branch with a similar structure and function. Both had a President, Vice President, Secretaries, etc. with largely the same powers.
- Prohibition of International Slave Trade: This had been in place since the early 1800s in the United States; slavery was legal between Confederate states with existing slaves, but no new slaves could be imported.
- Emphasis on State Rights: There are a significant number of revisions which award states with expanded rights compared to the American Constitution, particularly in regards to business, trade and taxes. This also included provisions such as restricting taxes so that a state could not disrupt riverborne trade between states, i.e. each state had a right to enjoy the benefits of the Confederacy rather than one profiting at the expense of the rest.
- Limitation of Presidential Terms: The Confederate President would enjoy a 6-year term, compared to the American 4. However, the President could only serve a single term; prior to amendments in the 20th century, American Presidents were eligible (though unlikely) to serve an indefinite number of terms.
- Slavery: The Confederate Constitution did include a provision prohibiting laws "denying or inhibiting the right of property in negro slaves". This isn't saying "slavery is legal", it's saying "slavery cannot be made illegal".