I have used Leupold (Vari-X III 2.5-8X) and Zeiss and Swarovski. All were excellent and all offer good customer support. Leupold is not as bright and sharp as the Euro brands, but is very good and dollar value is high for quality received. Leupold's customer support is probably the best in the industry, although Zeiss has also treated me very well when a used monocular needed cleaning. They also replaced the objective ring on a 6X20B mono that I'd dropped, denting that part. No other damage occurred, although I dropped it on a brick driveway. Never dealt with Swarovski's repair people, although I'd be amazed if they aren't excellent to deal with.
I have heard good reports from Nikon owners, but my overall feeling is that you should buy the Leupold of the brands that you're considering.
I doubt that most people should be taking a shot at game animals beyond the range that 7X or 8X magnification allows. And don't neglect to set the 'scope at 2X or 3X for a great deal of hunting, especially where a close shot is apt to be the case, as with the coyote hunt described above. The wide field of view will be vital. This is especially so if you may encounter dangerous animals, whether you are hunting them or not.
Now that I think about it, I read almost everything that the late Jack O'Connor wrote about guns and hunting from the late 1960's-on until his death in 1978, including his books as well as his columns in, "Outdoor Life" and in, "Petersen's Hunting". I don't recall him ever using over a 6X 'scope. Ditto for Warren Page and John Wootters, to name two other major writers. I can't recall any famous gun writers who've used high power scopes on hunting rifles. And O'Connor shot one elk at 600 yards. Even he, a superb marksman, felt that was stretching things, and he rested his .270 on a coat or something and fired from the prone position.
Military snipers kill people at extreme ranges, but few have their skills in both shooting and in range estimation. It is simply inhumane to fire at game at long range, over 400 yards for all but the very best shots, who can estimate range and wind drift very well, indeed.