For Lincoln, the highest priority was to preserve the union and try to avoid the war. When the war did finally begin, he understood that he can't allow the south to become independent so he had to go to war and give it everything that the North had because otherwise the south would become a serious threat and it had to be a part of the Union.
To Davis, the most important issue was preserving the agricultural economy of the south and to have the south secede and become an independent country as a confederacy of states. He wanted to keep the system that had been working for decades before it and didn't want to abandon the southern way of lifestyle or give the federal government any more power.