All types of rubrics (not just those created by students) are medium agnostic when the categories and descriptors are focused on learning, no tasks.
For example, an excerpt from a poor rubric might read, “The poster includes at least 6 facts about the state and is interesting to read.” In this instance, we have at least two problems, as (1) students must create posters to demonstrate their knowledge, thus throwing a great deal of choice/creativity out the window, and (2) a hidden emphasis on compliance (not learning) exists, as students know exactly what to do (include 6 facts) to receive the highest mark.
Meanwhile, from a rubric on an opinion/argument unit, a superior descriptor under the reasons/evidence category might read, “Multiple reasons support claim. Evidence is clearly stated and supports reasons with statistical numbers/data or stories. Audience is convinced!” What is of significance here is this descriptor (which was created by teachers during our professional development session) can be met however students choose: essay, TED Talk, radio show, etc.
What I have found as you work toward student led projects is that the students have a real tough time with the freedom at first. Without the experiences, students will need to be given a limited number of choices at first, lest they run into the paradox of choice.