Men do have two eyes and visual seeing is optimized for using both eyes|
Everyone can easily make some experiments using a binocular with just one or both eyes to see the huge difference. First there is the subjective magnification, it is bigger with two eyes than with one eye
Also you can see more faint details with two eyes, which are not visible with just one eye
While looking at the stars you will see more stars with two eyes than with just one, the ability of collecting light is increased by binocular viewing.
Usually one is talking of a factor 1.4242 or sqrt2 for the gain of magnification and the ability of light collection. Generally this factor is right for the increased magnification and for the increased ability to collect light for pinpoint objechts like stars. But when we are talking about extended objects, such as nebulae and galaxies with a low brightness of area things are different, were we do not only need a big ability to collect light but also or even more a lot of contrast.
And as contrast is increasing by using two eyes such extended objects have an even bigger benefit and the factor is more around 1.5 to 1.8 Especially when we are talking about contrast we have to tals about the differnt types of telescopes. An APO refractor is showing more contrast that a dobsonion and a dobsonian is showing more contrast than a Schmidt-Cassegrain with it's huge central obstruction. Another factor of binocular addition us the ability of our brain, to temporable compensate bad informations coming from one eye.
This is very interesting when it comes to poor seeing conditions, because the seeing conditions are never the same in front of both telescope tubes. Our brain is able to amplify the good images and to ignore the poor ones, and for this reason a binoscope is suffering less from poor seeing conditions. I did compare different objects with my 12,5" Portaball dobsonian with a 2" binoviewer and my Borg 125mm APO binoscope as well as with my Celestron C8 Binoscope
Even having the smallest aperture the Borg 125mm APO binoscope showed me galaxies and nebulae the best.
Even having a bigger aperture he C8 binoscope is way behind observing these objects because of the worse contrast caused by the huge central obstruction
For brighter objects like planets or globulars things are changing, here the C8 binoscope is able to use it's aperture and leaves the 125mm Borg binoscope behind.
The 12,5" dobsonian is at the end of the chain for all observed objects Beside weight, size and uncomfortable usage of a double dobsonian here we can see another disadvantage
Caused by the long and twice reflected light path to the eyepiece the double newtonian also needs a big secondary mirror which causes an obstruction in the same range of a Schmidt-Cassegrain
Just regarding the focal ratio and the exit pupil there remains an advantage of the double dobsonian, but at what price... Unfortunaltely we can not increase the size of an APO double refractor much bigger than 6" for technical and financial reasons.
And even here we are talking about focal distances of at least 1000mm, which are not really usable for wide field observations. Like in monocular astronomy also for binoscopes there is no single and universal best telescope.
I prefer the combination of two binoscope, a double APO refractor with high contrast and a short focal length for wide fields and a double SCT with more aperture and a longer focal length mainly for planets an globulars. Regarding the theories behind binoscopes Aries Otte has some very detailed and profound articles at his website of which I would just put the links here: Why a binoscope? binocular summation factor The WOW factor