The abilities of the eyes are determined by the users skill and there own training. Amaterasu was given to Sasuke by Itachi and in his other eye he implanted blaze control so that he could incorporate Amaterasu into has chidori and as an example Sasuke was able to use part of Susano'o before he had blaze control and Amaterasu. 

And to clear something up the user does not have to have Amaterasu or Tsukuyomi, they only have to master the two abilities that they chose to implant into there eyes through concentration and training which is shown when Kakashi uses Susano'o