The bit about "a brighter in low light" is correct, but I'm sorry to say, I totally disagree with the parts about better detail, better colour detail, and seeing in the shadows. They are not deliverable by a bigger objective.
Happy for others to chime in but there is one principle you need to understand. It doesn't matter if you are using an 8x20, 8x32, 8x42, 8x50 8x58 and so on, on a bright when your pupil is stopped down, to 2mm, every single one will be an 8x16 as far as your retina is concerned. Consequently, providing there is no difference in coatings and optical quality or stray light, they would have the same brightness, same resolution and same colour rendition. If we are really very picky, the bigger binoclars will be slightly dimmer due to thicker glass.