There are a number of ways to discuss API popularity. Our metrics are based on developer engagement. The "track" functionality on ProgrammableWeb lets developers declare an interest in receiving updates on particular APIs. Which APIs and categories are seeing the most activity.
DuraSpace has announced that the Fedora community is currently working on the initial phases of drafting a Fedora RESTful API specification that is better aligned with W3C and other modern standards such as the Linked Data Platform (LDP), Memento, WebAccessControl, and Fixity on ingest.