1841 is when the Neu-Groschen was introduced, although it seems the decision was taken in 1840. However, it's clear that Thaler on the standard of 1/14 of a Cologne Mark were issued from 1839, so a split at that year would allow all coins to sit entirely within one currency or the other, since none were issued before and after that year.
It is a little bit of a fudge but I think the gap in the production of any low-value coins just about justifies it.
One other thing. I used the term Neu-Groschen as that's what appears on the coins but all our entries have Neugrochen, as does the link above. Given our recent discussion on the Silbergroschen, perhaps these are better?
Thaler (1806-1839)
12 Pfennige = 1 Groschen • 24 Groschen = 1 Thaler • 1⅓ Thaler = 1 Conventionsthaler
Thaler (1839-1873)
10 Pfennige = 1 Neugroschen • 30 Neugroschen = 1 Thaler (Neugroschen introduced 1841, Vereinsthaler after 1857)
Former Numista referee for banknotes from Ireland, Northern Ireland, Scotland, Wales and Saint Helena.