The Constitution of the Confederate States was adopted in 1861 and was the law of the Confederacy from 1862 until the end of the Civil War in 1865. It was in many respects similar to the US Constitution. The Confederate Constitution provided for a House of Representatives and a Senate, and members of each house were chosen in a similar manner to US representatives and senators. In addition, the Congress of the Confederacy had similar powers to those of the US Congress, including collecting taxes, borrowing money, coining money, organizing the militia, and other similar powers. Many of the rights granted by the Bill of Rights (the first ten amendments to the US Constitution) were also granted by the Confederate Constitution, including freedom of religion and speech and the right against unreasonable search and seizure. However, the right to own slaves was stated directly in the Confederate Constitution (and of course this right is not part of the US Constitution).
The Confederate Constitution also provided for a president and vice president chosen by electors in a similar manner to the way in which the US president and vice president are chosen. However, unlike the US president and vice president, those in the Confederacy were chosen for six years (instead of four years). The president was, like the US president, the commander in chief of the army and navy. The Confederate Constitution also established a Supreme Court.
Unlike the Constitution of the US, the Confederate Constitution mentioned "Negros" and slaves by name. Representation in the Confederacy was apportioned based on three-fifths of all slaves, while the Constitution of the US stated that representation was based in part on three-fifths of "all other persons." The Confederate document forbade the importation of slaves from other countries and stated that the Congress could forbid the importation of slaves from territories and states other than those in the Confederacy. The Confederate Constitution also stated that a slave who escaped or was carried from one state or territory to another in the Confederacy had to return to the place where the slave's labor was due and to the slave's owner.
I think that both the Constitution and the Confederacy spoke to union of states. The Constitution was driven by the need to "form a more perfect union" and with the idea of states remaining together and being represented as such. The Confederacy was driven by a similar idea in that Southern states felt their voice being invalidated and a need to have this represented drove the development of the Southern union. The South believed that that Constitution was a compact, a voluntary agreement that was not binding. The North saw the Constitution was permanent and not something that one can join and disengage whenever seen fit. I think that this helps to bring out a major difference between both the Confederacy and the Constitution. The Constitution sought to make clear what the focus of a nation should be and provided a framework for this government as a statement. The Confederacy was more of a reaction to what was happening. The Constitution's emphasis on rules, regulations, and procedures was something laid out and designed in detail at the Constitutional Convention. The Confederacy was more of a response that was driven by passion. The technical elements of governance and procedures were not as strongly worded because of the emotional contagion of the time. In this lies another strong difference between both of them, as well.