In short: most of the evidence that supports the validity of Nanotyrannus is suspect, and likely not indicative of a distinct genus.
In long: the following traits have been used to support Nanotyrannus’s validity:
- The two skulls have more teeth than Tyrannosaurus skulls. Gorgosaurus and adult Tyrannosaurus have variable tooth counts between individuals, in the latter seeming to decrease with size; it’s probably not distinctive of a different species.
- The holotype skull has a differently-shaped braincase. The braincase was crushed during fossilization in this specimen.
- Jane has proportionally longer limbs. Albertosaurus has proportionally longer limbs as a juvenile, and the difference is likely not indicative of a different species.
- Paleontologist Thomas Carr goes into it further here.
And it seems suspicious that both Nanotyrannus specimens are juveniles (Jane was 11 years old, and the holotype skull is about as mature) and, among the army of Tyrannosaurus specimens, there would be no other Tyrannosaurus from around that age range.
Note: the Dueling Dinosaurs specimen is in private hands and is effectively scientifically worthless, so I haven’t discussed it here. But that specimen doesn’t necessarily entail much for Nanotyrannus – if the holotype skull is a juvenile rex, Nanotyrannus lancensis isn’t valid, and Dueling Dinosaurs would be a different species.