I do not see any value in the new inbox.
It's not refreshing immediately to show the last sent message, you have to go out of the thread, then come back to see it.
For a new booking it does not have an easy option to select between channel or sms,
It only shows sms or channel messages, not email and system messages.
Each time I need to click on Activity Timeline, then click on full view to have a conversation through the good old inbox.
It takes me two extra clicks each time to view any message.