The important part are the consequences and follow-up actions based on the feedback.
I have been part of a 360 through FC and then a different system as a my regular annual eval.
In both, the consequences and the method in which the results are communicated are the most important factor. I suggest spending a majority of the time on the process for which consequences will be implemented.
I would analyze the evaluation tools based on the perspective of which are most likely to enable clear and positive followup actions. The tool that does that is the most valuable.
In my case, the 360 asked more specific questions. It created the most value because I had more specific feedback on which to take action.