Check out this link: Civil War battle statistics
Note that Lee's casualties were sometimes, but not always, higher than his Union opponent's.
I think a bit of analysis would ask: who was on offense, who was on defense, and who won the battle. The results could well explain the differences in casualties.
BTW, it's interesting in WW II that MacArthur has always been portrayed as the most "economical" of all the American commanders with the lives of his men. But the best of all was Nimitz, who had control of the central sector of the Pacific. Combined ground (island)/naval casualties under him were much lower than under MacArthur.