So the paradigms -- NX-class vs. [Ship Name]-class; numerical registry for a particular class in order of production vs. general registry of "NCC" and testbed ship registry of "NX" -- seem completely different between the FSF and UESF.
But that's just it -- the Federation is a different nation from United Earth. Different nations use different vehicle registry prefixes. NCC is for Federation ships. Simple. (True, some of the Daedalus
-class ships in the Romulan War
books were referred to with NCC numbers, but they were also given the anachronistic "U.S.S." prefix, so the given designations may have been erroneous.)
However, I recently saw Doug Drexler say something on Facebook about how the intent was for Enterprise
to remain NX-01 because it would always be a testbed for new technologies, so even though it was used as the class name, apparently the creators' thinking was that it did represent the experimental/testbed designation even at the time.