Cartoons dont need too much computing power...
I mean... NMS even works with PS4 VR... this speaks volumes about the gfx qualities of the NMS Cartoon Show
Here's where you are wrong, NMS still uses PBR and all the SFX that Odyssey uses, that part should be the same in terms of performance, not only that, but NMS uses voxel based terrain rendering which is leagues more resource intensive that the heightmap rendering that EDO uses. To pile on a little more the cartoony effect also takes some extra post processing that EDO doesn't use. Don't let the pretty colours foul you, under the hud, NMS is as complex (or even more) than EDO when it comes to rendering. The mayor difference is style, not necessarily complexity. Beyond that, a huge difference would be texture size and poly count. I can't speak for poly count but in terms of textures, the old textures inherited from Horizons look really bad, even with texture quality on high, NMS doesn't have this problem with a few exceptions I have found on my experience.
I almost forgot, in NMS you even have player made bases and terrain modifications, because of the nature of this being user generated content there are some shortcuts (like using occlusion planes as Odyssey does). Other comparison point is how populated NMS terrain is compared to EDO, the more there is the more you have to render, the more intensive it is. If you look at NMS screen shots you can notice that there is waaaaaaaay more stuff to render than in EDO.
When you bring all this to the table, EDO should be running even better than NMS does, there are clear problems with the performance, some people in the community has already detected some of this issues like overdrawing and poorly written shaders.