Translation:Our boss is annoying.
Right, I'd say both are possible. 麻烦 is troublesome, e.g. the person often comes to you with new demands. There's a more colloquial term with the same meaning in Beijing dialect: 事儿 ("我老板很事儿"). 烦人 is annoying, e.g. the person keeps talking to you about something you don't want to hear, and you find that very disturbing.