But there are also prospects for each company to grow domestically. In North America, Kors ranks third among the top 10 handbag brands in terms of sales, at 9 percent, while Kate ranks eighth at 2.2 percent. Though sales have fallen off in the past two years, Coach still leads the category with a substantial 22 percent share of the market.
Read MoreGucci who? Michael Kors gains ground in Europe
Last month, Barclays issued a report on the opportunities U.S. luxury brands face compared with their typically higher-priced global competitors. It predicted that U.S. luxury companies will outperform the global luxury space from 2013 to 2016, offering significant room for both Kors and Kate.
Aside from these opportunities, Citi said Kate Spade stands to gain from its ahead-of-the-curve digital positioning, the potential for licensing in new categories and a new pricing strategy that includes more handbags at opening price points around $200, as well as more expensive price tags on the higher end of its assortment.
Still, the analysts did not count out Kors. They noted that the label was the most preferred handbag brand among nearly half the responses in one of Citi's recent national surveys. They also highlighted the company's potential to grow its men's business to $1 billion, from an estimated $300 million, as well as an opportunity in e-commerce, which is currently outsourced to luxury department store Neiman Marcus.
Read MoreBurberry still a hit, currency headwinds loom
And although Citi expects the brand's same-store sales growth to moderate, it still predicts they will increase between 15 percent and 20 percent through the year ending in March 2015. It predicts Kate Spade will also continue to grow its comparable-store sales by double digits through the same time period.
"We still expect Kors to achieve and beat guidance, but to a lesser extent than historically," the report said.
Citi has a target price of $42 on Kate Spade, which is currently trading near $34. It set a $107 target on Kors, which is currently trading around $92.
—By CNBC's Krystina Gustafson.