Based on this question and an answer, it appears that although almost all southern white men of draft age were in the military during the Civil War, only about half of northerners were. For those in the north who didn't serve, I wonder what was the most common reason that they weren't drafted.
Both north and south allowed people to pay for substitutes, although the south ended up drafting those people anyway when it got desperate. It seems unlikely that paying for replacements would account for a very large number of men, since it cost a lot of money. Substitutes seem to have been an emotional issue in the New York City draft riots, but it's hard to believe that it was numerically very common.
Were there exemptions for various reasons in the north, but not in the south? The north had more immigrants. Were non-citizen immigrants not drafted?