The most fundamental similarity between the Reconstruction plans of Abraham Lincoln and Andrew Johnson was their common insistence on the primacy of presidential power. Both men believed that the president should manage the process of Reconstruction. Congress had other ideas, though. One faction in Congress, the Radical Republicans, had strong convictions about Reconstruction. Congress always had the power to admit territories as states into the Union, so it claimed the right to manage the readmission of the states in the South, too. The Supreme Court also could play a role; it had passed the key Dred Scott decision before the war on the slavery question.
Neither Lincoln nor Johnson wanted vengeance. Their conciliatory policies welcomed rebels back into the united nation. This is unusual because defeated rebels were typically—according to historical precedents—put to death or imprisoned after failed rebellions.
Lincoln was assassinated in 1865 before he could implement much of his plan for Reconstruction. Had Lincoln not been killed, it is probable that Reconstruction would have been largely handled by him as president. He was the respected and successful wartime leader, and he would have been able to persuade Congress and run Reconstruction. Johnson, on the other hand, lacked Lincoln's stature and flexibility; he was not even a Republican. Because of Johnson's limitations and misjudgments, Reconstruction was ultimately managed by Congress.
Lincoln's and Johnson's plans were both conciliatory and moderate in their treatment of the South, but Johnson was considerably easier on the former Confederacy. Lincoln's Ten Percent Plan called for readmission of Southern states after a mere 10% of voters pledged allegiance to the United States. Congress insisted that half of the voters needed to pledge loyalty first. Johnson, upon becoming president, did not even adhere to Lincoln's 10% threshold. Southern states easily and quickly formed governments under Johnson's plan. Johnson also did not protect black people's rights as Lincoln had done. Lincoln would have worked with Radical Republicans to safeguard and buttress the right of former slaves, but Johnson did not really care about them.
Southern states responded to Johnson's leniency by passing the so-called black codes, which created differential punishments for formerly enslaved people versus the wider population. Also, black people were intimidated by the Ku Klux Klan and killed in race riots in the South. Enraged Radical Republicans took over the Reconstruction process and impeached Johnson partially due to his incompetence.