There are both similarities and differences in terms of the optics between binoculars and using the longer focal lengths of a Superzoom camera to view distant objects.

First, let's look at the similarities:

• Focal Length. Both the binoculars and the camera use optics to enlarge distant objects. If a binocular has a magnification factor of 10x, that would equate to roughly a 500mm focal length (35mm FF comparison), since a 50mm lens on a FF camera yields about the same image size in the viewfinder as the unaided eye would see.
• Entrance Pupil. Both the binoculars and the camera would normally have larger entrance pupils that the opening of the iris in the human eye, which ranges from about 2-3mm in bright light to 5-7mm in the dark. This allows them to gather more light being reflected by the distant objects which allows the magnified image to be brighter than it would be if a smaller entrance pupil were used. Even here the binoculars start to pull away a little as a 10x50 set of binoculars have an entrance pupil of 50mm (times two - one for each eye), which is quite a bit larger than the entrance pupil of a typical superzoom camera at 500mm focal length (35mm/FF equivalent).

Now, let's look at some of the optical differences:

• Angle of View/Field of View (FoV). The image in the camera's viewfinder, and also in the resulting photo, at longer focal lengths is restricted to a very narrow FoV. Again using 35mm FF equivalents, a 500mm lens yields a FoV of around 5°. At 1,000 yards a 5° FoV translates to around 260 feet. In other words, you could see two objects that are both 3,000 feet away in the same FoV if they were no wider than 260 feet apart. In comparison, a typical set of 10x50 wide angle binoculars such as the Orion UltraView has an FoV of 341 feet at 1,000 yards.
• Full Image Circle. The camera truncates the image circle of a lens to a (usually) rectangle. The maximum FoV is only possible along the diagonal of the frame. Binoculars allow you to see the full circle of the FoV and thus the maximum FoV in all directions. Even if a camera and binoculars have the same FoV, the binoculars allow you to see 1.7 times the area at the same distance because a camera with a 3:2 ratio only displays about 59% of an image circle with the same diameter as the diagonal of the rectangular image sensor.
• Image Brightness. The exit pupil of a decent pair of 10x50 binoculars is around 5mm. This allows them to be used in fairly low light, including astronomical viewing, without amplification. They allow you to directly view the subject optically. Most Superzoom cameras, on the other hand, use an electronic viewfinder. While this allows the image to be amplified, it also introduces problems of limited resolution introduced by the resolution of the EVF and electronic noise that would make the experience of using them for astronomical or other low light viewing much less satisfying.
• Stereo Vision. Binoculars allow both eyes to see slightly different angles of the same objects that allow use of depth perception. Other than specialized 3D cameras, most cameras are monocular.

Some of the non-optical differences:

• Batteries. All digital cameras need a source of electricity. Usually this is supplied by a battery that needs to be constantly recharged or replaced. Most binoculars don't. You can store them for months, years, or even decades and they are ready when you need them. You can also use them non-stop forever without worrying about the batteries going dead because they don't have any batteries to go dead!
• Environmental Factors. Most binoculars are made to withstand fairly robust weather conditions and other environmental factors such as dirt/dust/sand and extreme temperatures much more severe than even the hardiest professional grade camera bodies.