DSR is somewhat similar to supersampling, it allows you to render the game at a higher resolution than your display, lets say at 3840 x 2160 when your screen supports just 1920 x 1020. The rendered image is then scaled down to fit the target display, thereby improving the visual quality.
The benefits are the same. The extra sample info improves every pixel—not only does it smooth object edges, but it also oversamples texture info, shader effects, the works. The performance hit is the same, too. The GPU will perform like it would when rendering to a 4K display, perhaps a little slower due to the overhead caused by scaling the image down to the target resolution.The site concludes DSR can offer noticeable and sometimes even dramatic improvements in visual quality. The combination of 4x oversampling for every single pixel and soft scaling to reduce temporal noise delivers stunning results, but is obviously very taxing on your hardware.
The twist with DSR is that it can scale images down from resolutions that aren't 2X or 4X the size of the target display. For example, DSR could render a game internally at 2560x1440 and scale it down to fit a 1920x1080 monitor. That's just... funky, if you're thinking in terms of supersampling. But it does seem to work.