I am planning to buy a new DSLR and am comparing two models. One of them has a fastest shutter speed of ¹⁄₄₀₀₀th of a second while other has a limit of ¹⁄₈₀₀₀th.
I know that a fast shutter speed will help me to capture fast moving objects, but I want to know in which scenarios I would be using a shutter speed which is faster than ¹⁄₈₀₀₀th of a second.
In most scenarios the extra stop between 1/4000 and 1/8000 second will make very little difference in terms of freezing motion. 1/4000 will freeze all but the fastest objects you are likely to encounter, and even 1/2000 will freeze world class human athletes and most animals at typical shooting distances.
Where the extra stop will come in handy is when you are in very bright light, have already adjusted your camera to the lowest available ISO and want to use a wider aperture to reduce the Depth of Field (DoF). If you find yourself shooting in such situations often, you will probably wind up eventually acquiring and learning to use Neutral Density (ND) Filters. These reduce the amount of light entering the camera without adding a color cast (hopefully) in order to enable slower shutter speeds and/or wider apertures when desired. Once you start shooting with ND filters the difference between the two camera's fastest shutter speeds will not mean much.
Having said that, there are often other features that differ between such models. In the case of the Canon 5D mark III versus the Canon 6D, for example, the 1-series focus system of the 5D3 is worth the difference in price compared to the less capable 'prosumer' focus system in the 6D, but only if you need the faster, more accurate, and more consistent focus system. On the other hand, the 6D includes built-in WiFi and GPS. If you need those extras, it will cost quite a bit to add them to the 5D3 via external modules.
In normal conditions this doesn't matter at all.
1/8000 does have it's uses - mostly super-fast sport at close range, but even formula 1 race cars (photographed from a safe distance without a super-telephoto lens) don't show much motion blur at 1/500.
Unless you photograph sports from up close both 1/4000 and 1/8000 are faster than you'll need, my guess is that the two models you are considering may have some differences that you should care about but the max shutter speed isn't it.
