A couple of comments gleaned from Flayderman's Guide.
Although there were 200,500 Model 1860s made, the shoulder stock notches and fourth screws were dropped around ser. no. 50,000. So, I don't see how they could be more rare.
During the War, most production went to the army (US) but after the war, the fit and finish of "civilian" models is thought to have been improved.