I'll start by playing devil's advocate. First, there's certainly no question that Lincoln served as commander-of-chief during the most brutal conflict in U.S. history. To use Satanovsky's term, the American Civil War was indeed "vicious" (as civil wars so often are): At least 620,000 fighting men died on both sides -- at a time when the U.S. population was 31 million. (For what it's worth, so far 36,000 Syrians have died in the conflict there, in a country with 20 million people.) While most of the fighting between the Union and the Confederacy took place between regular military forces, Lincoln's Civil War also set a grim 20th-century precedent by explicitly drawing civilian populations into the hostilities. We don't know how many civilian casualties were caused by the war, since no one kept track, but the numbers probably weren't trivial.
Some Union tactics, indeed, were designed to inflict harm on civilians. General Philip Sheridan pursued a scorched earth policy in his efforts to pacify the Shenandoah Valley. General William Tecumseh Sherman wrote a letter to a fellow general in which he explained the plans for his famous "March to the Sea" in 1864, in which he set out to destroy the South's military infrastructure by laying waste to the civilian economy:
We are not only fighting armies, but a hostile people, and must make old and young, rich and poor, feel the hard hand of war, as well as their organized armies.
Sherman also gave his commanders carte blanche when it came to retaliating against "guerillas or bushwhackers," as well any "inhabitants" who dared to impede the invading Yankees or "otherwise manifest local hostility" (a description that leaves a lot to the imagination). Under such circumstances, he instructed his army commanders to "order and enforce a devastation more or less relentless according to the measure of such hostility." However you slice it, this doesn't exactly sound like population-centric counterinsurgency -- more like a recipe for cracking heads.
Assad's defenders would presumably assert that the Syrian president hasn't done anything worse. Assad himself claims that his government is not really fighting his own people. The enemy, he says, is a bunch of terrorists sponsored by foreign powers.
And what about Satanovsky's charge that Lincoln would have been typecast as a "vicious tyrant" if he lived today? Many people at the time, in fact, made just such accusations about the 16th president of the United States. He was commonly assailed as a "dictator" for his suspension of the writ of habeas corpus, his declaration of martial law, and his expansive use of executive powers. For many southerners, of course, his opposition to secession was enough in itself.