Not sure how it works but based on this write up it would seem they is more to it than a basic filter.
Known as Radeon Image Sharpening, AMD’s solution is an intelligent sharpening technology that provides a lift in the visual quality of a game without a dip in performance. The effect takes a look at the high contrast parts of any given scene in a game and artificially draws out more detail. AMD says this sharpening of textures makes 1080p look close to 1440p when upscaled on a higher resolution monitor.
AMD showed a screenshot from a game and highlighted how Radeon Image Sharpening pulled out crisper details in the shadowy rocks from the darker aspects of an image without interrupting any anti-aliasing softening happening near the light source.
Unlike DLSS, which must be implemented on a game-by-game basis, Radeon Image Sharpening is a simple switch. According to AMD, it just works.
https://www.digitaltrends.com/computing/amd-radeon-image-sharpening-dlss-ray-tracing-e3-2019/
So it seems there is some kind of selective filter goes on so it isn't a blank sharpening kernel over the whole frame. Nvidi'as sharpening likely doens't do that but that would just be a minor driver release; use a contrast filter to produce a salience map to weight the USM. By sharpening high contrast areas you can avoid some artifacts in low contrast areas and potentially increase performance. That is all completely standard image processing.
But this just reinforces that AMD is not doing any kind of upscaling at all, simply sharpening. So DLSS is still an entirely different technology.
Maybe Nvidia will put out a new driver with some sharpening improvements