I'd say that depends on the retention requirements of the recording folder and the public folder.
If you symlink "./public/recording" to "./recording", the public file only exists as long as the original file exists. Some automated cleanup could result in unexpected file deletions from "public/" (or, more specifically, the creation of dangling symlinks). However, this might be a use case for a hard link if you need the file in both places and both directories are on the same filesystem. Though I haven't thought about the implications of a hard link in this case enough so far.
If you symlink "./public/recording" to "./recording", the public file only exists as long as the original file exists. Some automated cleanup could result in unexpected file deletions from "public/" (or, more specifically, the creation of dangling symlinks). However, this might be a use case for a hard link if you need the file in both places and both directories are on the same filesystem. Though I haven't thought about the implications of a hard link in this case enough so far.