Honestly, as a native of (urban) NC, I felt like TX was very similar when I visited. And the few Texans I went to school with didn't seem to feel too out of place in NC either. We've both got nice people, growing and diverse cities, a solid college education system, and super religious people everywhere just to keep you on your toes... Really the biggest differences I could tell was that TX got hotter and you have crazy long stretches of road with nothing at all on them (which is indeed a uniquely western thing).
But I think the whole concept of "deep south" vs the "new south" is where you see the differences come into play. Charlotte, Raleigh, Durham, Asheville, and many other NC areas, are great, diverse places that have far more in common with Dallas/Austin/Houston than with whatever the stereotypical image of "the south" is that most folks have in their heads. So in other words, I think TX is just as southern as NC is, and that isn't necessarily anything to be ashamed of.