The unlocked version adds some useful features.

Themes

In the settings you can choose between 4 different themes

Download Music

You can download ("Make available offline") songs, artists, albums, playlists and the current play queue.

During the download process you have to select an existing playlist into which the downloaded files should be added.
Songs are downloaded into /mnt/sdcard/Music by default. You can change the folder in the settings.
Note: As far as I know android does not allow writing files to an external sd card in recent android versions. Therefore you will not be able to download your music files to an external sd card

Local music player

The unlocked version allows you to use music pump kodi remote as your local music player

You can play music stored on your android device
You can stream music from your android device to any of your configured Kodi instances
You can stream music from your android device to chromecast

PVR

The PVR section has the following features

Browse and play tv and radio channels as well as filtering by channel groups
Play PVR recordings.
Note: Due to limitations in the json-rpc api it is currently not possible to delete PVR recordings from the app
Browse channel EPG
Start / Stop recording channels
Note: Due to limitations/bugs in the json-rpc api it is currently not possible to schedule future recordings from the EPG

Shortcuts

The unlocked version contains a grid with some useful shortcuts when swiping the remote up

Note: To customize the shortcuts see customize shortcut buttons

Streaming to another Kodi instance

In the unlocked version you can select on which running Kodi instance files should be played

On the remote select a Kodi instance
Select the Cast button in the action bar. A dialog will be shown containing all running Kodi instances which you have configured. Select the desired device on which you want to play your files
When starting playback of some music or videos inside the app they will be automatically streamed to the Kodi instance that you have selected. It also works for content of many addons as long as they are configured on both devices
If you have selected local playback this feature will only work for music files. To stream movies or tv shows you have to go to the details screens and select the stream button from there

Kodi Queue

The application has two different queuing implementations. Both modes have some advantages and disadvantages. The Kodi Queue is only available in the unlocked version

Local Queue:

This queue is only used for Music files that have been scanned into your library. The queue is stored locally on your device
It allows instant switching music playback (local / remote playback) without loosing the queue
If another family member plays start playing something on Kodi your queue is still present on your device and you can simply resume playback
Some additional queuing options not available using Kodi Queue
There is a small gap between playing tracks

Kodi Queue (requires unlocker):

If this option is enabled the play queue on Kodi will be used. Therefore multiple users can modify the queue from their devices
The "cast" button is disabled in this mode. You need to switch to local queue before you can stream files again
If you use the files section to queue music files (or multiple videos) you will probably want to enable this mode since you won't see the Kodi Queue content if using the local queue