While research continues to investigate and improve the accuracy, fairness, and normative appropriateness of content moderation processes on large social media platforms, even the best process cannot be effective if users reject its authority as illegitimate. We present a survey experiment comparing the perceived institutional legitimacy of four popular content moderation processes. We conducted a within-subjects experiment in which we showed US Facebook users moderation decisions and randomized the description of whether those decisions were made by paid contractors, algorithms, expert panels, or juries of users. Prior work suggests that juries will have the highest perceived legitimacy due to the benefits of judicial independence and democratic representation. However, expert panels had greater perceived legitimacy than algorithms or juries. Moreover, outcome alignment -agreement with the decision - played a larger role than process in determining perceived legitimacy. These results suggest benefits to incorporating expert oversight in content moderation and underscore that any process will face legitimacy challenges derived from disagreement about outcomes.