1080p at the same screen size will have visible pixels. These will be 'softened' on the 4k set but even if bi-linearly filtered, it'll look no worse, and in reality you'll have a decent upscale algorithm filling in the missing data with something reasonable.
According to DF, 1080p upscaled to 4K constantly looks worse than non upscaled 1080p on a 1080p display.
http://www.eurogamer.net/articles/digitalfoundry-2016-samsung-ku6400-4k-tv-review : "4K content looks stunning on the KU6400, but when it comes to 1080p and lower resolutions it's worth pointing out that 4K screens in general deliver a softer presentation than a native 1080p display, with more artefacts when viewing at fairly close distances, and the KU640 is no exception. Full HD material still looks excellent on the 40-inch KU6400 screen, mind, with 1-1 pixel details perfectly preserved across test patterns and in Blu-ray movies.
You do lose the pixel-perfect sharpness of a 1080p display, though, which is to be expected, but the upscaling is at least reasonably clean, with very slight soft-focused jaggies only becoming visible when sitting very close to the screen. As such, 1080p games still hold up very well, even though they don't look as good as on a 1080p screen."
http://www.eurogamer.net/articles/digitalfoundry-2016-panasonic-dx750-4k-hdr-ultra-hd-tv-review : "Upscaling is somewhat mixed with 4K displays, with lower resolutions appearing softer and less defined compared to native 1080p screens."