..Eh, the more I look at One Piece and Fairy Tail side to side, the less they seem to resemble each other. And that's really where the similarities end. There are plenty of goofy, laid back shounen protagonists, so to write Natsu off as a Luffy clone is unfair.
...I can definitely see the Dragon Ball inspiration in both series, though. Both Oda and Mashima are DB fanboys that drew in "Toriyama" style growing up and evolved from there.
That said, I really can't see Luffy and Natsu fighting for any reason other than a misunderstanding. Not only are they in completely different 'professions', they're similar enough that they'd probably bond pretty well.