Hmmm good question. 지금 just means now, at this very moment. 지금 집에 있어요. 이제 implies that there is a difference with the past: 예전에는 커피 너무 좋아했는데 이제는 싫어졌어요. It can also imply a result from a past action: 할 일 더 이상 없어서 이제 갈게요. Compare the next two sentences: 할 일 아직 많은데 지금 가야 해요. I still have many things to do (here), but I have to go (home) now. 할 일 아직 많은데 이제 가야 해요. I still have many things to do (at home), so I have to go now.

Refer to http://www.italki.com/question/280050