The same set of actions will be performed whether you invoke the shutdown.sh or shut down from the Admin UI. This includes stopping listeners, shutting down packages, and stopping the various subsystems(JMS, GD etc).
The Admin UI lets you schedule the shutdown after waiting for the specified time.
The shutdown script can be included as part of another script through which it can be executed automatically.
With Command Central , you have additional means of starting/stopping an Integration Server.
Based on your usecase , you can pick what suits you.