Does Firefox have a built in flash player? I do not think so. I had to install Adobe Flash plugin-in from the Software Centre and it worked with Chromium as well. So, the issue of being unable to play/replay TV programs (BBC Player, ITV Player - UK TV companies) is the same for both Firefox and Chromium.
I wonder how things will turn out when the Dash becomes a fully functional search engine. Will clicking on a TV channel open a web browser or a video player? At the moment it opens the default web browser at the TV company web page. Which will not play without Adobe flash player for Linux installed.
Thinking about this, (I know I shouldn't think. It overheats my brain) that session would have been more beneficial discussing how to help the Chromium developers get pepper flash into Chromium. After that happens will be the time to recommend Chromium as the default browser and it would be because it is open source and does not require additional user interaction to get videos playing.