The ideal size of the objective lenses for an all-purpose pair of binoculars
The decision is based on two cardinal issues: The purpose of the big lenses at the front of a pair of binoculars, as well how heavy the binocular is going to be.
The big lenses at the front are for gathering light, which is the single most important element in how a binocular functions. The bigger the lenses, the more light enters the instrument, but bigger lenses weigh more and this leads to a bigger instrument. Smaller lenses are not that heavy, but on the downside, let less light enter the instrument. So manufacturers have looked for a golden mean between enough light gathering ability and not too much weight for an all-purpose pair of binoculars and the result is a binocular with objective lenses of 42 mm.: They feed in lots of light in bright daylight and let enough light through for reasonable viewing at dusk or dawn, when it's overcast or in the forest, but have only a moderate effect on the overall weight of the instrument.
How powerful should a versatile binocular be?
The magnification of ordinary size binoculars vary from 6x to 12x; giant binoculars go as high as 30x. You do get some in-betweens as well, like 8.5 and 10.5. Power of 9x is associated only with big lenses of 63 mm.
6x magnification power is too low and 7x is better, but still not powerful enough for a versatile binocular. On the other hand, more magnification power like 10x and 12x has certain implications: You will have the joy of more magnifying power, but the first implication of more power is a less bright image. Furthermore, higher magnification is also associated with movement sensitivity. The slightest motion, like normal hand tremors is amplified making finding an object (in particular when it's moving) very tough. More power inevitably means a smaller field of vision, which in combination with the problem of movement sensitivity, makes focusing on an object even more difficult. The depth of vision of the instrument is also impaired, so the viewer has to keep his finger on the focus wheel in particular if the objects moves towards him or further away. For this reason watching birds quite close is difficult with a powerful binocular.
The magnification which is a near-perfect compromise between the extremes, is 8x. It is powerful enough to make you see distant objects and to see a lot of detail the closer the object gets. However, 8x is not too powerful to let you suffer from the negative features associated with high magnification mentioned above.
The exit pupil is the stream of light passing through the binocular at the eye pieces. The exit pupil is determined by dividing the objective lens diameter by the magnification: 42/8 = 5.25 mm. With the same apertures (42 mm.) a 10x magnification gives you an exit pupil of 4.2 and a 12x magnification 3.5 mm. These will all be enough in bright daylight, but when the sun is fading, in overcast conditions or in a darker environment like a forest the smaller exit pupils will let too little light through to deliver a relatively clear image for the viewer to observe.
Optical glass and coatings
The best compromise for an all-purpose binocular (8x42) will not be your ticket to perfect viewing; the glass used for the lenses and prisms as well as the optical coatings have to be of the highest quality.