There’s more to binoculars than just objective diameter (the 23) and the magnification (the 8x). Monoculars will be the same- they’re just basically one half of a binocular.
Objective diameter is a rough guide to the amount of light the binoculars can gather- this will be important in low-light and night conditions.
Binocular design and materials is important as well. Porro-prism binoculars give the best image quality for cheap binocuars, but roof-prism ones are lighter and more compact for the same objective diameter and magnification. Materials play a big role too- the prism glass type is important- BAK-4 glass is what you want- it has nearly total internal reflection, giving brighter images than BK-7 glass. Another construction detail that is very important is the type and degree of antireflection coatings applied to the optical surfaces. Since every bare air-glass surface reflects about 4% of the light hitting it, this can build up pretty quick in binoculars, causing lower light transmission and washed out images. Manufacturers apply coatings that reduce this phenomenon- “coated” optics usually have magnesium flouride, which reduces it to 1.5% per surface, and “multicoated” have a mix of compounds that reduce it to something like .25%. There’s also a difference in how many surfaces are coated. Basically there are 4 types:
“Coated”. This means that some surfaces are coated with magnesium flouride.
“Fully Coated” This means that all surfaces are coated with magnesium flouride.
“multicoated” This means that at least one surface is multicoated, and (probably) the rest are single coated.
“fully multicoated” This is the best- all air-glass surfaces are multicoated.
There’s also exit pupil diameter, which is basically the objective divided by the magnification. This is the diameter of the shaft of light coming out of the eyepieces. So for 10x50 binoculars, the exit pupil is 5mm, and for 7x35 it is 7mm. This is important mainly for astronomical binoculars, because under lower light levels, your pupils open up to about 7mm, and you want to get as much light into your eyes as you can, hence the popularity of 7x50 or 11x70 for astronomical viewing. Exit pupil can also have some implications on daytime viewing- generally, you won’t need a huge exit pupil because your pupils will be constricted so that you won’t need much of an exit pupil- 8x23 binoculars are more than adequate for bright daytime viewing since your pupils will probably be around 2mm anyway.
And finally, there’s eye-relief. This is how far from the eyepiece lens that you can see a full-width focused image. If you don’t wear glasses, this is not much of an issue, but for glasses-wearers, this can be very important, since short eye-relief glasses are tough to use with glasses.