Well, I sometimes feel like "the" Newfoundlander on Fodors (I'm not the only one of course, but my screen name is the definite giveaway!) so I figure I might as well reply.
I attended university in the Maritimes & lived in AB for over 3 years, so I've had occasion to think about this a little, and I have a multi-part answer.
First, we're unique because we had a period, which ended within living memory, in which we were effectively our own country, and many still think of ourselves as Newfoundlanders first, and Canadians second.
Second, that idea is possible because Newfoundland still has at least the remnants of a culture (and that's not a derogatory statement--there are many parts of Canada where I see very little that qualifies as Canadian culture on a daily basis). We have a unique history, our own music, folklore, proverbs, idioms, and literature. There are very few Newfoundlanders who do not feel attachment to and pride in some of these aspects of our culture. I think the only other province where this applies, is Quebec.
Finally, geography cooperated: the island is...an island, and heaven knows Marine Atlantic has done its bit in keeping us remote. Labrador was even less accessible, until recently truly isolated.
I only hope the ubiquitous internet memes and American rap stars don't swamp our stories and sayings by the time the next generation takes over.