I have ran across these two words being used in some articles and blog sites. It seems they both translate to "work", but when and why would you use one over the other?
作業 is closer to tasks or procedures, which can be 'finished' in a few minutes or a few days.
仕事 refers to both small tasks and lifelong vocations.
If you want to ask someone's occupation, you can say "あなたの仕事は何ですか?" but not "あなたの作業は何ですか?" (well, let's forget about honorific expressions for now). When you look at a calendar and want to check what you have to do today, you ask yourself, "今日の仕事は何だろう?" or "今日の作業は何だろう?"