In this fight I would bet my money on Cover-More. NIB is a strong performer in the health insurance business, but Cover-More has been achieving faster growth at a company level, growing earnings per share by 20.7% in the first half of the 2015 financial year, compared to NIB’s 4.4%.
http://www.fool.com.au/2015/04/15/is-nib-holdings-limited-a-better-bet-than-cover-more-group-ltd/