ILya (
@koshkin ) is really going to be the resident expert on this stuff, but I will give this a go. There are all kinds of relationships with optical design and doing one thing impacts another. The objective size, the focal length, the erector range (magnification) are all going to play a part. Look at the majority of 8x42 binoculars out, the FOV varies with almost every manufacturer, but then take the same manufacturer and the same model line and now look at their 8x50 bino and what do you see, the FOV is typically less on the 8x50 vs the 8x42. For a technical discussion on why, that is for ILya. But here's the thing, it's different for most manufacturers and based on how they design the optic to begin with so just because larger objective may generally mean narrower FOV, you have to look at the specs of a given optic and compare based on that as the differences may not be as far apart. Can a manufacturer make an optic with a larger objective that has greater FOV, yes they can and have, again it's all dependent on the optical formula and what compromises they're willing to make in order to meet their objective. For example, take the Vortex Razor HD 8x42, this bino only has 388' at 1000y, but take their newest design Razor UHD 8x42 and it has 420' at 1000y... same magnification, same objective but one design has much greater FOV than the other.
The same goes for rifle scope designs, you have the general rule but then you see exceptions to that rule and now you're beginning to see manufacturers offering wide angle eyepieces to get greater FOV (e.g. Burris XTR III, Nightforce NX8, new March High Master scopes, Leica PRS et al) whilst still utilizing large objectives (56mm). But sometimes you sacrifice something else in trying to reach one objective, maybe its edge sharpness, depth of field (DOF) or you wanted a short scope design but realize you have to sacrifice other features in order to get a short scope.
Regarding eye relief, here again we have a general rule, but does it have to be that way, or put another way, could a Japanese manufacturer create a huge eye relief binocular? Certainly, as to why they don't I do not have the answer, but we are beginning to see Japanese designs encroach closer and closer (and in some cases surpass) on the European dominance and it's not so cut and dry anymore.
The binocular world is a bit different from the rifle scope world and there are different aspects to design at play with one of the biggest being recoil, so manufacturers have learned to design rifle scopes with enormous eye relief (compared to binoculars). Again, how much eye relief is dependent on the design itself and really has nothing to do with east vs. west. One other aspect that is not related to eye relief but has an effect on our perception is "eye box" this is something you will not see listed in any specs because multiple factors come into play with the optical formula but this is typically where you see the alpha optics (both rifle scope and binocular) excel. I define eyebox as the ability to easily obtain a full sight picture when getting behind an optic. So while eye relief might dictate that proper eye position is going to be around 3.54" from the ocular lens at the rear of the eyepiece it doesn't tell you how forgiving that scope is going to be to deviations from this distance, so two scopes may both have 3.54" specs, but one is much more forgiving than the other. For me personally, a forgiving eyebox is more important than eye relief unless eye relief happens to be really short for a given scope and you're shooting magnums. One other note on eyebox, a scope that may have a finicky eyebox can be more pleasing to use when you mount the scope properly and practice to get proper cheekweld every-time, with these techniques, even some of the most finicky scopes can be tamed to a large degree.
Here's an image identifying what getting a full or clear sight picture looks like and what a finicky eyebox tends to induce (shadowing, etc.)
In summary, both European and Japanese manufacturers produce some amazing optics these days. FOV can be a huge benefit but it may not be the end all be all requirement, there are many factors at play with optical designs and it's unfair to make blanket statements. Our sport is one of compromises, we make them with almost every choice we make. So while giving up FOV to gain a larger objective may at first sound detrimental, if you are one who frequently shoots in low light situations, that sacrifice may be well worth it and so forth.
