What is "Stress my GPU"?
What is this tool useful for?
The stress testing tool can be useful for checking whether an overclocked GPU is running stable over a longer period of time (a.k.a. without crashing / blue screening your operating system) and to see how your GPU, CPU and PC handle thermal loads (as in their ability to cool themselves while running at peak performance). If you really want to test your computer's fans (or just use your PC as a really expensive heater), you can even stress test the GPU and CPU at the same time.
The benchmarking tool can be used to measure a GPU's (and CPU's) performance relative to other devices as well as for detecting performance degradation due to inadequate cooling or hardware malfunctions. Since the benchmark measures your GPU's or CPU's ability to do highly parallelizable math calculations, it could be useful for quickly comparing the performance of running similar workloads (e.g. GPU-based cryptocurrency mining) between different devices.
Does the stress test have any limitations?
Since "Stress My GPU" is web-based, it's restricted to what the browser you're using thinks is OK for a regular website to do. So while the stress test can indeed max out your GPU's processing utilization, it has limited ability in pushing every single part of your GPU to its maximum limit all throughout the stress test. Due to the aforementioned restrictions, testing multiple devices would require you to run "Stress My GPU" on multiple browsers, each of them using a different GPU (or CPU).
What about the benchmarking tool?
The benchmarking tool faces the same restrictions imposed by browsers that the stress testing tool does. In addition, different browsers may be better or worse at running the benchmark's code and as such yield higher or lower scores with the same GPU (or CPU). Furthermore, the tool is focused at measuring the performance of a very specific highly parallelizable math computation. Said computation workload is also synthetic (meaning it's not necessarily indicative of real world workloads). So if you're serious about measuring the performance of your devices, this application shouldn't be treated as the be-all-end-all source of truth but as a quick indicator used as part of a larger benchmarking effort.