The BSI camera sensor of the Desire 820 packs an f/2.2 aperture. At the same time its bigger brother, the One (M8) is endowed with a 4MP Ultrapixel camera on its back which works in concert with a sensor that is collecting depth data for the image. The camera sensor of the One (M8) has an aperture of f/2.0, which allows more light to get inside the sensor itself (at least on paper, that is). They also have the same focal length - 28mm. The cameras of both smartphones have somewhat similar bags of features, such as autofocus, digital zoom, geo-tagging, and the usual bunch of functionalities that you'd expect them to flaunt.
We took some sample photos with both devices here at IFA 2014, and it's up to you to decide which one performs better. Still, take into consideration that these are preliminary, so don't jump to any conclusions based on these just yet.