My carpetted stairs, both to basement and upstairs, have the standard nosing. The original carpetting on the upstairs stairway was "waterfalled" but the basement stairs and replacement carpet on the upper stairs is "nosed". It looks different, but no difference in climbing the stairs.
Strange that in North America a nose is REQUIRED on closed riser stairs under 11 inches (depth of tred) and in Australia, for instance, the nose is NOT ALLOWED.