I only agree with this part here:
And for brotherhood, huh...There are nothing like Winchesters! Salvatores are like 0.001 against 100.
The Salvatores come nowhere close to the Winchesters!
As for The Originals, I like Tyler, but I didn't really want him or anyone from Mystic Falls to end up in NOLA. But I see why Tyler would fit into the story. I think the biggest issue with taking Caroline to NOLA would be trying to make her fit into the story. If she goes, she would only probably be left as part of a romantic relationship and frankly I would hate a character like Caroline to be reduced to just a relationship just as I would have hated the Originals remaining in MF and just being part of relationships and nothing more (i.e. Kalijah, Mabekah). Tyler fits into the story for what they have- him wanting to avenge his mother's death but I think the writers would bring in other TVD characters once they can fit them into the greater story. In The Originals, all of the characters are linked to one huge dilemma. There is no side story. If Caroline or anyone else from TVD show up, they would have to contribute to the entire story at large. I can see the possibilities with Tyler but I just don't see it with Caroline or any of the other TVD characters.