I love the idea of new characters and new situations- while remaining faithful to the spirit of the original series. Nothing can change how I view or feel about the original series, the '91 version didn't. I liked that version, too, what I remember of it in it's short time on air.
I would watch if they remade the original version or made it more like the '91 model. But I'd prefer to not be able to reasonably know what's going to happen next in a certain storyline or compare any particular scene to how it was done back in '68 or whenever. However, I wouldn't mind thinking- "How would the original Barnabas deal with this new character of the '04 version?" or "How would this new '04 situation work if it occured before the original Quentin was introduced?" Who knows, maybe some of the original actors can portray some of the new characters?
I agree with Raineypark that "multiple storylines are more compelling and intricate and viewers like stories to come together like puzzles." I think there would have to be a certain number of self contained episodes as well. Or that's just my guess for an hour long show in prime time these days, though I may be wrong.