The problem is probably that either file isn't encoded correctly, and the server isn't set up correctly.
Here is a portion from an article I wrote for InDesign Magazine. This portion was drawn from the InDesign Help file. Notice that a QuickTime .mov file is NOT supported for streaming in InDesign CS5/5.5/6.
Streaming video files reside on a Web server or on a Flash Media Server or Flash Streaming Service. Streaming video files must be in a Flash video format or H.264-encoded. To set up your document for streaming video, start by creating an empty frame or select a video you want to replace. Choose Video from URL from the Media panel menu. Specify the URL and click OK. Note that the URL must point to a file that ends in the appropriate file extension; for example, http://www.fakeURL.com/videos/Intro_Video.f4v for a file on a web server. Use rtmp:// in the URL for a video on the Flash
Media Server or Flash Streaming Service.