Maybe it is clear from my question that I don't know much about lenses, both on binoculars and super-zoom cameras, for example I don't know how can I compare the light that enters a binocular with a camera.
Binoculars are identified by two numbers (eg. 8x42) where 8 is the magnification and 42 is diameter of the objective lens, the one in the front of binocular, the bigger it is, it will allow more light and results in better image. I also know the basics of the lenses on cameras, bigger sensors and bigger aperture means brighter image.
But since I haven't got a super-zoom camera, nor a binocular, I have no idea why people pay for binoculars when they can get a super-zoom camera like Panasonic Lumix DMC-FZ70 for lower price and much higher zoom?