Taken as a whole, actual combat deaths for either side cannot be compared to the much greater death toll attributed to disease etc. But in combat causalities, the North suffered many more than the South.
The NRA of today was birthed in 1871 as a direct response to faults which arose during the civil war. In that war, as a whole, the superior marksmanship of the average Confederate troops (more rural) was far superior to those of the Union Army. (more urban)
In battles of the western campaigns, the rural western army troops of both sides were much more evenly matched as to having a lifelong familiarity with firearms and being accurate with same, and the causality ratios reflected this.
The NRA’s purpose was to correct that acknowledged accuracy imbalance of the civil war, to encourage and teach marksmanship for all American civilians, especially the young.
http://www.nrahq.org/history.asp
Major reason had little to do with shooting skill.
To win, the South had only to avoid losing. They therefore, especially after Gettysburg when most of the casualties occurred, normally fought on the defensive from behind fortifications. When Lee first took command, his troops called him Granny Lee because he was always making them dig in. It is to be expected that assaulting fortifications will be more costly than defending them, that's the whole point of digging in.
Due to the more constricted terrain, there was less room for maneuver on the eastern front, and much more trench warfare than in the west.
Many exceptions, of course, to these generalities.
When counting casualties, keep in mind that Lee frequently didn’t turn in correct casualty reports. The south couldn’t stand the truth. His whole army was nearly gone already at Appomattox Courthouse. Some he had shot for desertion, and then didn’t report the number he had shot.