And they both go to show that statements/calculations about things like urban density are heavily influenced by historically and culturally determined political boundaries and definitions. Even look at the US Census Bureau 80% urban metric that a lot of people like to quote. Lots of small towns with farmlands and orchards (like where I live) are "urban" by this particular definition. And they are "urban" relative to truly rural Wyoming. But they're not urban in the sense of having any of the attributes of a dense city center.
There must be a way to come up with an (almost) universally applicable metric of city-ness, regardless of the adminstrative boundaries, that can be applied to situations like this map. Something like, the area in which the population density is above a certain threshold, and the population that lives in that area.
FiveThirtyEight has done some work in that area for purposes of splitting urban/rural from a political perspective. The article also mentions a couple other examples of something similar.
Although it's often even messier than that. Look at the density of Manhattan vs. NYC as a whole. Or core Paris vs. Paris as a whole. Much less the many American cities with fairly dense but small downtowns but that sprawl far into the distance.
Both have their places, but I wouldn’t say one is more misleading than the other. One is administrative and one is more demographic.