This is another of those mid-game / late-game facility matchups. In this case you must have a Research Hospital built before you can have a Nanohospital. Individually, they both do exactly the same thing, and together they do twice as much. Like most of these 'second generation" facilities, the Nanohospital is quite expensive to maintain.
Since it comes at a time when your production (and therefore
your population) may well be surging from the addition of Soil
Enrichers to your territory, its anti-drone influences are likely to be important
to maintaining stability in a base trying to reach full population and production.
Of course, an extra boost to Labs is useful any time.