Question: What is the differences in use of these two objects? 

**Which one should be used for a "Youtube-like" video player with a custom skin and playlist?**

Answer: 
FLVPlayback is a component that already has the controls - scrollbar, play/pause button...etc. Video object is an object that only has the video area.

If you want to do something like the YouTube player, you will need to start with the FLVPlayback component and skin it [(Example)](http://www.adobe.com/devnet/flash/articles/custom_flvcomp.html). But you will have to build a playlist by yourself or use the List/DataGrid components in flash.
"Component" really is the key word here, Video is the base object, the FLVPlayback Component is a UI wrapper that uses the Video object internally. It provides a simple interface for developers to add video content, with user controls, to their applications.