The NIT had a higher percentage of ranked teams. In addition, several of the NCAA teams had made the NIT their first priority--playing in the NCAA the week after the NIT, with some of them playing underclassmen to give them experience.
Also, you should know that no teams with black athletes (such as Seton Hall) were invited to the NCAA. Teams with black players were regularly discriminated against in both the polls and by the NCAA tournament at the time. Not so with the NYC based NIT.
The short answer though, is that post WWII through 1953 or 1954, BOTH the NIT and NCAA were considered national championship awarding tournaments. You can go through year by year, and make a case for the champions of either. But in the national eye, both tournament winners were called National Champions in that era. Prior to WWII, the NIT was the clear heavyweight, no matter what Ute fans will tell you about Red Cross Charity matches.
Look no further than my sig pic for an example of a contemporary source calling the 1951 NIT a National Championship. And there are many others, including the New York Times.