The mintage of the 1867-S Dime is slightly larger than that of the 1866-S, and their prices track almost identically up to EF, but beyond that the 1866-S becomes the more valuable of the two. This is surprising because the number of Mint State examples of each is almost the same, and they both top out at the same grade -- MS65.
The entire mintage of the 1867-S Dime came from two different die pairs, according to Liberty Seated Dime expert, Gerry Fortin. Both varieties appear to be of similar rarity, thus the die life appears to be approximately 70,000 coins for eacg oibverse -- not a bad output. Both varieties share the same reverse, making it the real workhorse with an output of 140,000 coins.