Energy & performance comparison: GPU mining vs playing HD Video
Using a GPU to mine Bitcoins would use a lot more power than watching HD video, since while the video decoder would only use the processing power it needed, a Bitcoin mine would use all of the power available to it.

I don't have any real numbers, but I think mining Bitcoins would be equivalent to, say, playing Far Cry 3 on the maximum settings, while watching HD video would be more like playing Fallout 3 on medium settings.