I think the biggest thing about the Inhumans is that they are this race with a very established culture and government system. They have their own traditions and for most of their existence, they seemed to be ok with staying in their own little corner.
Now, all of a sudden their city gets destroyed and their population grows exponentially. There are inhumans all over the world, yet very few of them have any knowledge of the traditions of their own people. "Nuhumans" have stopped belonging to normal human society and at the same time have no knowledge of Inhuman valors and lifestyle.
Inhumans should be a book about "original" inhumans trying to re-establish an Inhuman nation at a time their race seems more scattered than ever. I'd view this book as a metaphor for nations trying to keep their culture in the era of globalization. It should be a book that's much more about cultural identity than it is about oppressed racial minorities.
X-men, on the other side, should be about oppressed minorities fighting for social inclusion. They shouldn't be trying to distance themselves from society, but to become an accepted part of it. I think that should be the big difference.