I have read a few studies about this matter as it is a topic of interest to me. Surprisingly enough, I have found a variation in opinions. Recently I finished two books on women and finances/career. One book was by Sheryl Sandberg, where she talks about the glass ceiling and gender pay gap with facts and figures. And another by Money Penny where she describes why the gender pay gap is just an illusion. This might still remain a topic of debate for generations to come. But if you ask me whether women should be paid less for the same work, the answer is a definite NO.
Although this also largely depends on the nature of work… If it is physical labour job, then I suppose there will be a difference because nature has gifted us with different biological strength and this may indeed make a difference in the work performance if you compare the two sexes. Thus, I believe the reward should largely depend on situational factors and individual performance rather than gender. It should not be a battle of the sexes but rather a battle of performance.