[chris lewis]

Hi

The Crux is about 6 degrees. 'Most' 10x50 binoculars will have around approx. 6 degree TFOV. [True FOV].
Field of view is related to magnification, as the magnification increases you will get a corresponding smaller field of view, [in general]. Hence the 20x50 will give you a 'narrow' FOV like around 3 degrees but with twice the magnification.
The greater the magnification the smaller the FOV, hence you inability to see Crux in the full with a 20x50 bino.
Field-of-view is the size of an area that can be viewed from edge to edge. If two people were standing 1000 yards away from you, one was to your left and one to your right and the distance between the two people was 300 feet, then your field-of-view would be 300ft at 1000 yards while looking through the binoculars.
Most binoculars will have this sort of measurement on them. [or in Mtrs.]
310 ft. at 1000 yds. is approx 6 degrees FOV.
A large field of view is especially desirable in situations where the object viewed is likely to move, or when the user is moving. A 7x50 or a 10x50 binocular will give you a wider image and these powers are good for hand holding and general dark sky sweeping. A 20x50 will need to be tripod mounted and will give a more close up view but will show much you a smaller amount of FOV. [A 20x50 will also give you a dim image - a 20x70 will give you twice the brightness.]
Power affects brightness. Other things being equal, the higher the power, the dimmer the view.
An average 7x50 has a 7.1 degree Tfov, a large 25x100 has a 2.4 degree Tfov.
Don't forget a 20x50 bino is twice the power of a 10x50 bino. The 20x50 Bushnell has the highest power then the other two you mention.
You may have heard of 'Apparent' FOV [Afov] this the 'breadth' of the actual image you get in the eyepieces. Afov is the power of the binocular times the magnification, so a 10x50 binocular will give a 50 degree Afov.
40 degrees Afov is very narrow, [like looking down a toilet tube roll] 50 degrees is acceptable, 60 is desirable and more then 65 degrees is considered a 'Wide angle' FOV. [Some say 60 degrees.]
The wider the FOV will usually give you more edge distortion so there is a trade off. The better quality binoculars will usually give you less edge distortion and a better quality image.
It can get complicated and I may have got things wrong but read up more esp. on this subject the info here and on 'Cloudy Nights'.

Chris