The biggest issue is that it’ll really vary quite a lot of the specific. POM cost can vary greatly while Nanite is fairly consistent regardless of inputs. Anecdotally, I have found that a well optimized POM material with shadows performed similarly to Nanite when occupying 100% of screen space.
Visually, both had pros and cons, but overall I would say Nanite was the winner. This is because while technically POM offers per pixel displacement which is arguably superior to per vertex displacement, this is counteracted by losses due to artifacts (either stairsteps of not dithering samples or blurriness of dithering).
Nanite being sharp and artifact free was enough to set it above.
I found an unoptimized POM material will perform worse than Nanite (for example using trilinear filtering on the height map will significantly increase hidden sample counts and slow down the material a lot).
POM is also harder to naturally blend across materials of a landscape, because there is no guarantee that the heightmap will intersect at the blend point, causing floating artifacts.
Also as mentioned previously, Nanite will natively support shadow mapping - POM shadows are quite hacky inferior.