Two factors largely account for the Union's heavier casualties.

Army of the Potomac, pre-Gettysburg: The Army of the Potomac, the United States' largest and best-known army during the Civil War, had a remarkable run of middling-to-terrible commanders during the first half of the war. In succession, the army fell under the command of a career officer promoted above his ability (McDowell), a timid egomaniac (McClellan), a political appointee who was shockingly inept (Burnside), and a career officer who lost his nerve after landing on the receiving end of Lee's most impressive victory (Hooker). These officers presided over a series of major defeats that did significant damage to the Union's commitment to staying in the war.

Army of the Potomac (post-Gettysburg); any army under Grant: the technology available during the war heavily favored the defenders, as they had time to level rifled muskets and explosive artillery at tightly-packed ranks of attackers. After Gettysburg, the Army of the Potomac was more or less constantly on the attack. This was also the general posture of any army commanded by Ulysses S. Grant. Grant realized early on the Confederates did not have the logistical or manpower resources to recover from a sustained battle, and realized that following a defeat of his army with a retreat only further demoralized is men. As such, he favored to keep the pressure on the enemy, taking casualties in order to inflict some of his own. This strategy eventually stretched Lee's army beyond the breaking point as the two squared off around Richmond, securing the collapse and surrender of Lee's once-terrifying Army of Northern Virginia.

Source: McPherson, Battle Cry of Freedom