In my opinion the differing transition of power from Moderator to Administrator, and Administrator to Super Administrator is that you need more leadership qualities. Basically, as a lead team member you're going to be put into situations where you need to deal with staff on staff conflicts and be able to resolve them without escalating the issue or expanding it. In my opinion you're doing a good job as an Administrator, however you should show some of these leadership type qualities by speaking with staff and guiding/helping them out.

Good luck!