The TV series didn't explain it well, unless I missed it. In the trial, it appears cottontop admitted to first degree murder by the prosecution using his simple mind against him. Randolph McCoy wasn't to happy about hanging Cottontop post trial as the real killers were the one left to live with life in prison.
Mounts seems to have been rather gullible, at least: his confession was easily gotten out of him, with no deal being made for leniency. This is in contrast to Wall Hatfield, who was quite articulate on the stand in his own defense. There was also some confusion about just who was present during the shooting, and by confessing Mounts clearly could be marked as guilty. In his unsuccessful appeal to a higher court, Mounts' lawyer also said that the emotional testimony of Sarah McCoy had overly influenced the jurors .
Virgil C. Jones : The Hatfields and the McCoys