First you have to consider battles that are similar in nature, i.e. size of comparable forces, weather conditions, duration, results of combat(is the vanquished routed or still an effective fighting force?)
A routed army’s loss cannot be separated from those received in fighting. Often then only the victorious percentage is a valid comparison, especially since most ACW fights were not followed up with mercilessly with cavalry.
But we don't
have to match comparable battles, because if the casualties are different then one possible reason would be battles that
are not comparable.
If ACW battles tended to produce similar casualty figures to Napoleonic battles but there was no cavalry pursuit typically involved, this would mean perhaps that ACW battles were less
decisive (which I'd agree with, by the by) and that ACW armies typically didn't
include the capacity for pursuit as a matter of course, but it would not change the casualty figures which was the claim in the first place.
Similarly if ACW battles tended to see the victor taking almost as many casualties on a % basis as the loser, that would mean perhaps that ACW armies are less capable on the attack; it doesn't change the number of people who get killed or otherwise become casualties.
Chickamauga is most like Wagram imo. Two days of heavy fighting with the victor unable to pursue.
CSA 27%
French 10%
Figures are from Henderson
I didn't ask for you to line up specific Napoleonic and specific Civil War battles; otherwise I could point to the Waterloo campaign on one side of the ledger and the North Anna on the other.
I asked you for a Civil War battle and I'd point to a Napoleonic battle of comparable or greater size with a similar casualty count.
So at Chickamauga both sides suffer about 27% casualties.
Eylau sees both sides taking 20%-40% casualties (depending on estimates) which at the middle (30%) makes it an almost exact match. Eylau is also about the same size, or a little larger (75,000 per side instead of 60,000 per side).
The Waterloo campaign (which is a four-day campaign) of course sees Napoleon suffer about 50% casualties and the Allies about 25% or a little less.
It seems fundamentally self-evident that if ACW battles are beyond expectations for Napoleonic battles
we should expect there to be ACW battles which are on a different level to Napoleonic ones. There should be at least one, if not several, which have no Napoleonic battle of similar size with a similar casualty rate.