Jefferson Davis made a very hard fought attempt to lead the Confederate States to independence, which given how lopsided the resources pools were that both sides had to draw from, was a uphill climb all the way. And he knew that going into it. He was not a smooth, charismatic politician, but he was able to rally the people on more than one occasion. And he had the friendship and trust of his most capable general, Robert E. Lee, which made a big difference.
Where I think Lincoln was able to outdistance Davis was in two areas. Leaving aside the much vaster pool of manpower and resources, which there is no doubt was one of the deciding factors, Lincoln ultimately became much more ruthless in his conduct of the war, and he was willing to make the move towards freeing the slaves and elevating them in society, which was a tectonic shift in the social landscape of the day. Davis did reach that point, or at least had started down that same road, but too late to make a difference in the outcome. People talk about how Davis was obsessed with keeping the fight going when it should have been clear that all was lost, but Lincoln's determination to "save the Union" by casting aside of many Constitutional restraints and his willingness to go after the civilian population of the South doesn't seem all that different to me. He just succeeded in his goal, while Davis didn't.