The library database files contain the actual file data, all view configuration and playlists. A normal library restore from a library backup file would have restored these as well.
The MC16 application data location may contain some new folders and files that don't exist in the MC14 application data location. Other than that I don't see anything incompatible in the MC14 application data files. The actual settings (i.e. practically anything you can set in "Tools > Options", "DSP Studio", and "Playback Options") are stored in the Windows registry, not in the application data location.
Since you already renamed the folder, MC may have created the possibly missing files automatically, but you might want to reinstall MC16 on top of the current installation just to make sure that all needed files are present.
In general, if someone wants to preserve the already build thumbnail cache, that can be achieved by copying only two "application data" folders:
... \J River\Media Center 14\Library
... \J River\Media Center 14\Thumbnails
To
... \J River\Media Center 16\Library
... \J River\Media Center 16\Thumbnails
-- assuming only the default library in the default location is in use. Close both MC instances and remove the existing MC16 Library and Thumbnail files before proceeding.
EDIT
The MC14 application data location may contain also the "Cover Art" folder. This is the default storage location for the actual cover art files. The possible library links to this location will not be changed and the image files will not be moved automatically. It is possible to use the "Cover Art > Save Cover Art To External Location Specified In Options..." tool for relocating and relinking the image files.