You can tell that Xigbar has a certain air to him that leans towards the lighter side. He's... 'whoopsy-daisy', 'now, do you think that's fair?', 'you've put Organization XIII in quite a pickel', 'As if!'. Everything from his words to his 'totally, dude' surfer attitude and voice gives him the image of being a bit more, excuse the pun, light-hearted. That doesn't mean that he doesn't take his missions seriously, or that he's a complete goof off, like most think Demyx is. It just means that he has his own way of doing things that might not coincide with the way that Xemnas wants things done.
Saïx is 7th in the Organization. Xigbar is 2nd. Hence the question of Saïx being second-in-command, or so it seems, because, if we go by their numbers alone, Xigbar should be the second-in-command, and not Saïx. However, Xigbar does not act like he's second-in-command, although, neither does Saïx, really. Saïx more acts like a... lackey, who will do whatever is asked. A good personality for being second-in-command, but that doesn't necessarily mean much.