The Confederacy in 1861 was stronger relative to the Union than the 13 Colonies in 1775 or the 13 Free and Independent States in 1776 were relative to Great Britain.
But George Washington, who initially sought a decisive battle, soon realized that he didn't have either the muscle or the tactical skill to win such a battle. So he kept the Continental Army intact, struck where he could, as at Trenton and Princeton at the turn of 1776-77, and awaited foreign assistance, which the Continental Congress was working on with France and Spain. And eventually he wore the British down, and they quit.
I think too many Southerners (for their own good, that is) assumed that, because they were stronger relative to their enemy than the Patriots had been, they could win independence by decisive victories on the battlefield. They won victories in 1861-62, in the East, but warfare had changed since the Revolutionary War. The introduction of the rifle-musket changed things the most. It made battles more expensive, and made it harder for the attacker to win, because he couldn't get through the 200-300-foot-deep killing zone as nearly as quickly as RevWar soldiers could get through the 50-foot-deep killing zone of their war. Also, better antipersonnel ammo was developed for the artillery, and it could employ it for that entire killing zone as well. So the attacker, even when victorious, generally took much heavier casualties than the defender. Lee in particular won victories, but they were victories that the South could not afford. Antietam (Sep 1862) was the clearest example. It was a tactical victory, of sorts, but a decisive strategic defeat.
The Confederacy's official strategy, to the extent that it had one, was to defend its perimeter. A defense in depth would have been wise, because the Confederacy was huge and could theoretically trade a lot of space for time--time in which the northern public might tire of the war. But no state was willing to have its space traded for time, especially not the border states, who would be the first to suffer. So the Confederacy tried to defend its perimeter and succeeded more or less in the East at doing so. But the West was where the Confederacy would lose the war. Under the overall leadership of Albert Sidney Johnston, it invaded "neutral" Kentucky, inviting a response by the Union in superior force. Kentucky was lost, so Johnston next tried to hold Tennessee. His defeat at Shiloh killed both him and his chances, although it would be a long time before Union forces would control most of Tennessee. By the end of 1862, Grant was beginning what would become his brilliant Vicksburg campaign, which would culminate on 4 July 1863 with the fall of the "Gibraltar of the Mississippi," cutting the Confederacy in two.
Jefferson Davis wanted to detach major elements of Lee's Army of Northern Virginia to assist in the defense of the Vicksburg region, but Lee convinced him that it would be better for him to launch a second invasion of the North and win a big battle on northern soil, fatten his horses on Yankee fodder, and bring home weapons, equipment, food, and escaped slaves. Instead he was defeated at Gettysburg. After that, all the Confederacy could hope for was that a Democrat would win the presidency in 1864.
Gettysburg has been called "the price the Confederacy paid for Robert E. Lee."
The northern public was very war-weary in 1864, and Grant's expensive (in blood) Overland Campaign was heavily (and wrongly, IMO) criticized. Lincoln thought he might not even be renominated, much less re-elected, and told his key subordinates that they would have to win the war by March of 1865, because the incoming Democrat would have been elected on a platform of ending the war at any price.
But Sherman captured Atlanta, northern morale surged, Lincoln won re-election decisively, and the rest is history.
