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There is really not all that much directly relevant information that I can say about coatings, but it is useful to know why they are important.
There are all sorts of coatings used in modern optical devices and for a number of different things. However, in the context of riflescopes, when someone says “coatings”, they usually mean anti-reflective coatings, often shortened into ARC or “AR Coatings”. These coatings minimize the reflections at every air-to-glass interface. If you happen to be looking at a riflescope that has both lenses and prisms (like Trijicon’s ACOG, for example), then the lenses have AR coatings on them, while the prisms, depending on which surface you are looking at, will have either Anti-Reflective coatings, or High-Reflection coatings (one of the surfaces of the roof prism). However, for the sake of this discussion, I will stick to AR Coatings.
First of all, there is the natural question of why we need these coatings at all.
The reason is quite simple: every time light passes through an interface between two different materials (like air and glass, for example), some of it gets reflected back. The exact amount of light that passes through vs the light that gets reflected back depends on the specifics of the materials in question, but for air-to-glass and glass-to-air interfaces it works out to be ~4% per surface (if there are no AR coatings involved). A riflescope has quite a few lenses in it and, assuming they are air-spaced, each lens has tow surfaces that reflect a little light. Let’s assume that we are dealing with a scope of fairly simple construction, like some fixed power designs, and it has 5 lenses, i.e. 10 reflective interfaces. If you want to calculate the total amount of light that gets through the scope, you simply trace through each interface sequentially: first surface lets through 96% of incoming light, next surface transmits 96% of that and so on. The effect is multiplicative, not additive. It is more convenient to write that for a scope with 10 surfaces:
[Total light out of the scope]=[Total light entering the scope]*[0.96^10]
Incidentally light transmission is defined as a ratio of light coming out of the scope to the light entering the scope. In this case, from the simple formula above:
Light Transmission=[0.96^10]=0.665 or 66.5%
If you have some sort of a decent quality Anti-Reflective coating on every surface in the scope, reflection at each interface can go down to 0.5% (or conversely light transmission at each interface becomes 99.5%). In that case, for the whole scope:
Light Transmission=[0.995^10]=0.951 or 95.1%
In reality the calculation is not as simple as that since there is some wavelength (color) dependence involved in addition to other considerations, but even if this is a “back of the napkin” approximation, there is still a lot more light getting through when decent coatings are involved, ~30% difference in this case.
Pretty much all modern scopes employ AR coatings of some sort, so when you compare them the difference in total light transmission is likely to be not huge. Perhaps more importantly, your eye is very good for adjusting to these small differences in total amount of light that the scope delivers to it. In modern scopes, total light transmission is not directly important. As a matter of fact, it is a lot more important to know how much light gets reflected than how much gets transmitted.
While your eye does not care too much about light transmission, it cares about image fidelity a great deal. If there are strong reflections somewhere within the scope, you can run into a situation where there all sorts so of reflections bouncing back and forth inside the scope. Some of that secondary reflected light eventually makes it to your eye and your brain finds it more difficult to make sense of the primary image. On the surface, it seems like the strength of that secondary reflected light is a fraction of a percent of the original imaging getting through the scope, but under some conditions, it can have quite an effect on the image. For example, imagine you are trying to take a shot at a shaded target some time around sunset looking toward it. As you look through your scope, you have both the shaded target and the very bright setting sunlight in your field of view. Because the bright sky during sunset is so much brighter than what you are actually aiming at, even a weak reflection can be sufficient to seriously degrade how well your eye resolves the target itself (this is a type of optical flair, which I will touch on in the next section).
Riflescope advertising often proudly touts a high light transmission ratio of a particular scope. Higher light transmission (i.e. fewer reflections) is usually a good thing, but it should be looked at in proper context. Image quality is highly dependent on how sophisticated the optical design of a scope is, and top notch designs often require more optical elements than simpler ones. With so many lenses inside the scope, the overall light transmission might drop a little (remember each extra surface reflects some extra light), but the image quality of that scope is likely to be higher than that of a similar scope with less sophisticated (i.e. fewer lenses) design, if they use the same AR coatings. The best example of that is offered by two, no longer available in US, Kahles scopes that I had a chance to compare side by side: Kahles CL 3-9×42 and Kahles KX 3-9×42. Both are excellent scopes, but the more expensive CL has an extra lens in it. Otherwise, these are very similar designs that use identical coatings (Kahles’ AMV). KX had slightly higher light transmission, while CL has higher overall image quality.
Lastly, there is the matter of objective lens diameter to address. I often hear people say that because scope X has larger objective lens than scope Y, it has higher light transmission. That is not necessarily correct.
A scope with a larger objective lens lets more light into the scope. However, light transmission is a ratio that is normalized with respect to the amount of light entering the scope. Hence, while a scope with a larger objective lens may very well deliver more light to your eye, light transmission ratio is no tin any way effected by it.