The previous post was quite strong. I would like to amplify the answer regarding the notion of political vision on the part of both leaders. I think that Davis' government was more of a response than an actual political statement. The Confederacy seemed to be a response to the election of Lincoln. There was a sense of euphoria and elation as to the strike of "Confederate freedom." Yet, as with all celebration, a certain hue fell over the South afterwards: Now, what do we do? Davis and his government never quite took a hold of this issue. They had a difficult time charting out a political vision and enhancing the logistical concerns to make this issue a reality. In this light, Davis and his government suffered from a significant disadvantage over Lincoln's, whose government was animated by preservation of the Union and marshaling all of its resources to that end. In the end, this lack of vision and inability to see the war as a protracted conflict ended up crippling Davis' government, making it more challenging to govern and execute policy in an effective manner.
Two older books recommend to me are The Constitutions of Abraham Lincoln and Jefferson Davis, Russell H. Quinn, Exposition Press, 1959; and Two Presidents, Gilbert/Hudson, Naylor Company, 1973.
Two more recentbooks that I have read andliked are The Confederate Constitution by Marshall DeRosa, and A Government of Our Own by William C. Davis. Davis is accessible to a popular audience, Marshall almost so but some background in the subject is probably necessary.
I skimmed this and it looks good. It is only on Davis.
This contrasts the two Presidents. It is short and simple, but quality.
According to the historian John Keegan, Lincoln was a better war leader than Davis and his government was, in general, set up in a way that was more conducive to conducting a big war.
Keegan says that Lincoln's personal qualities made him better as a war leader than Davis. He says Lincoln was much better at getting a team of strong-willed men to go along with him. By contrast, Davis was more worried about always getting his way -- about always being right. He did not have the personal qualities needed to get cooperation.
The South's governmental system was generally "worse" than that of the North. Keegan points out that the South was based on states' rights. This led their state governments to dominate the central government. It made it difficult for Davis and the central government because the states did not want to send men, arms, and money out of their states to defend the national good.
I have based this discussion on Chapter 4 of Keegan's The American Civil War.