The Media Manager for WordPress consists of Media Libraries. You can upload images, video and audio. I am not sure what formats are accepted as there is no mention of it and I haven’t tried uploading anything except a picture. The big problem I find here is that there is no directory structure at all. If you want to put likewise images together for instance you need to find a plugin that will allow you to use folders. This is a complete and utter nonsensical approach because it doesn’t allow to use existing images in your file directory and arrange them in an organized way. The media can be incorporated in posts and pages using the Media Library by clicking on Add Media in a post/page.
The Media Manager is absolutely AWESOME! in Joomla but only for pictures. This is available in the Content menu as Media Manager and can be used in an article or anywhere else that has the editor using the same Media Manager interface (like in WordPress). The sheer greatness of this is that you can view your entire Images directory structure as well as create folders. This is an added advantage in case you use FTP to hoard an entire collection of photos for example. Any video or audio embedding will require an extension.
Joomla has some strengths and a weakness. WordPress ditto. Both can be overcome by plugin/extension. I will have to make this a tie even though I don’t personally have any need to upload audio/video and even if I were to embed a video, I would definitely not upload it – youtube anyone.