A good 80mm binocular is an excellent astronomical instrument, with an ability to reveal dim objects comparable to a low power 4 inch refractor. Magnification is the second choice to be made, and is co-determined by the field of view of the binocular. True field of view is the extent of sky viewed by the user, typically 6 to 8 degrees. Apparent field is the true field multiplied by the magnification, and is the viewing angle seen through the eyepiece. Modern wide field telescope eyepieces have up to 82 degrees of apparent field, but 60 degrees is also wide field and is found in some binoculars.
High power is no more useful than low power, it is a choice to be made by the user.
The main advantage of higher power to me is the wider apparent field it allows. Almost all lower power binoculars have oculars with much smaller apparent fields than higher power binoculars, to get a wide apparent field with a low magnification requires a very large ocular. It is similar to the limited apparent field of old 40mm eyepieces, where it looks like you're looking down a tube. I much prefer 7x to 10x for astronomy, they are noticably steadier and it is certainly easier to find objects in a wide true field. It can be useful to distinguish between the defects of an optical system.