We all have our own experience, and our own experience is our own reality, not to mention that no two of us have a pair of eyes built exactly the same.
I've read much on the various aspects of light and optics, but I find the theories expressed differ from my empirical observations...
Regarding the "7" formula
Ray B, I have personally used for close to 40 years (and continue to use) a pair of Zeiss 10x40 BGA binoculars. I have always found them perfect for my hunting purposes, including a fair amount of night hunting in winter as legal in Europe. Their light beam is 4 mm wide. I really never understood why a friend of mine carried the twice as big, twice as heavy, twice as bulky Zeiss 8x56 BGA at night, until I used them, side by side with my 10x40 for a couple hours on a moonless night... The "7" formula does not mean that optics with light beams less than 7 mm in diameter are not good, it simply means than they transmit less light then the human eye is capable of using.
To appreciate how much difference there is between 8x30, 10x40, 7x42 and 8x56 binoculars, or in other words 4 mm, 6 mm, or 7 mm light beams, there is only one method: use them side by side at nightfall or night. It is not very easy because few of us own a large number of high quality binoculars... But another and much easier way to experience the impact that a wider light beam has on crepuscular vision is to use a variable scope and progressively rotate the magnification ring up and down. It is quite an enlightening experience (pun fully intended) that cannot be appreciated until actually tried
And, truth being told, this probably does not mean much in America where hunting is limited by legal sunrise and sundown hours. The need for that wide 7 mm light beam is much more acute in Europe in countries where nigh hunting is allowed. It therefore makes sense that German makers focused heavily on this, while American makers generally ignored it.
I'm going with the Z8i for the 375 for the simple fact that my 5x Leupold is not enough for me at longer ranges. I consider my 375H&H to have an effective range of 300 yards on most PG. At that distance with my aging eyes, I need help that 5x can not provide. Not that the Z6i isn't good, but I questioned the price for getting just one more power of magnification. With the Z8i I can always dial back to 6x if I so desire and take full advantage of the 7 rule.
Regarding magnification
BeeMaa, I suspect that a lot of it has to do with acquired taste, rather than visual acuity. For the last century hunters (and military snipers) used 4x and 6x fixed scopes with perfectly satisfying results. The first major "revolution" was the quasi elimination of fixed power scopes for variables scopes. It happened in Europe in the 1970's I would say. Not sure when in the US. Maybe before? And it is only over the last two decades, since the early 2000's I would say, that magnifications have increased dramatically. Does it make shooting easier? Apparently a lot of people think so. How much is enough? Apparently enough tends to never be enough, if one observes market trends. The four scopes currently in the Zeiss flagship Victory product line are a perfect example.
Maybe I am a prisoner of my own paradigm and too rigid to change old habits, still owning a number of Zeiss and Schmidt & Bender 1.5-6x42 scopes, but I genuinely do not understand what purpose a 20x or 35x BIG GAME HUNTING scope serves. Sure they can be cranked down. I wear 1.5x readers as I type this, so my eyes are not as good as they used to, but I have never felt the need for more magnification than 6x for big game hunting even at 300 yards, although I do own a number of variables that go to 10x because it was what the market offered when I bought them.
Maybe I have the wrong expectations, and maybe I remain influenced from my youth by a lot of night hunting when aiming is done at an area rather than a point, but I certainly do not try to aim at an exact dime-sized point of impact when I hunt, because I know that I will never reach 1/2 MOA precision from field shooting hunting positions - this is just reality - so I have always been satisfied with magnifications that lets me aim at a 6" vital area behind the shoulder around the top of the lower third of the animal body. Unadulterated reality is that most folks - me included - pain to shoot much better than 3 to 4 MOA (3 to 4" circle at 100 yards)
standing from the sticks, or from various field positions, never mind off hands (!), so if my crosshair covers a dozen square inches at 200 or 300 yards at 4x or 6x I do not mind. On the other side of the argument, I have never missed an opportunity because I was struggling frantically to crank the power down when I could not find the animal in the narrow field of view of extra high magnification.
Truth be told, 6x or 8x are essentially the same
BeeMaa, and I fully agree that I do not see much of a point changing scope to go from 5x to 6x. I do see a major point though, going from Leupold to Swarovski (or Leica, Zeiss, Schmidt & Bender) but I readily admit a bias for German scopes (although Swarovski is actually Austrian).
In the end, and as usual, to each their own