Circumstances in which it would be appropriate to use HTML5

If you want a vendor-neutral format, to best respect viewers' freedom of software/hardware choice.
If you are running your video on low-end systems.
If you are looking to save costs (and not have to purchase Flash licenses).
If you want your video/application to be supported on the iPhone, iPad or other mobile Apple platforms.
If it is important that you work with an open development environment.

Circumstances in which it would be appropriate to use Flash

If your product needs to support a wide variety of browsers, including older models like Internet Explorer 6.
If you offer video streaming in several bitrates, and want clients to dynamically select between these based on network bandwidth.
If you do not want people to copy your content.
If you want to be able to splice in commercials dynamically throughout the video.
If you need integration with webcams and microphones for interactivity, like two-way.