The main difference, which is fairly obvious and perhaps overly so to be stated, is that Maxine is not Indian, wheras Moushumi is.  This difference, though blatant and obvious, actually plays a huge role in the novel, because there are many innate traits that come attached with it, and are what initially draws Gogul to them.  He is first drawn to Maxine because she isn't Indian, and has such a different lifestyle than the one that he grew up with.  Later, ironically, it is Moushumi's heritage and native Indian background that draw Gogul to her--it is such a stark contrast to Maxine.

Other differences relate to their personalities.  Maxine was very laid-back, not too driven, and rather easy-going.  Moushimi was pretty driven and ambitious, putting a lot of emphasis on her career, and on being noticed and important.  She cared quite a bit about her social life, her circle of friends, and her pursuits, often shunning family to pursue them.  Maxine was very close to her parents, and lived a more lackadaisical lifestyle that wasn't centered around ambition, but rather the seeking of pleasure.  Moushumi seemed bent on rejecting her cultural heritage and her family's traditions, whereas Maxine had no such conflicts and was at ease with her family and their traditions--so at ease that she still lived with them.

These two characters are a study in contrast, which makes it so much more interesting that Gogul ends up being in relationships with both of them throughout his life.  I hope that those thoughts helped; good luck!