Apple's new iPhone SE. Source: Apple.

Beware, Apple (NASDAQ:AAPL) and Samsung (NASDAQOTH:SSNLF) investors: Winter is coming. Until recently, both companies have been able to offset declines in computer and tablet sales with strong smartphone sales. More recently, investors have started to worry about smartphone sales as well. Analyst firm Gartner predicts that smartphone sales will increase only 7% in 2016, leading Gartner research director Ranjit Atwal to predict that "the double-digit growth era for the global smartphone market has come to an end."

In two of the three largest smartphone markets, the U.S. and China, growth will be even harder to come by, with Gartner predicting flat year-on-year smartphone growth. The second-largest smartphone market, India, is still predicted to have strong growth, but people in the country tend to buy lower-cost devices with razor-thin margins.

For both companies to overperform, especially in developed markets, Apple and Samsung need to increase their respective market share percentages. Increasing the number of users who upgrade to a new model would be a strong step toward growing market share.

Apple's upgrade percentage is higher than Samsung's
During Apple's last conference call, in January, CEO Tim Cook pointed out that 60% of people who had an iPhone in September 2014 still hadn't upgraded to a newer phone. The time frame in Cook's comment was important, because 2014 is when Apple rolled  out the larger iPhone 6 and iPhone 6 Plus iteration. Slowing upgrade cycles were blamed for the iPhone's flat unit and revenue growth last semester. Recently, Apple has introduced the smaller, cheaper iPhone SE to encourage upgrades.

Samsung would love to have Apple's 40% upgrade clip. A report from Kantar Worldpanel points out the differences between the two companies: Samsung's upgrade rate between February 2015 and January 2016 was only 26%.

There are a few caveats: Apple's time frame is a little more than one year and includes two phone iterations, while Samsung's is exactly one year and does not include the newest Galaxy S7 and Galaxy S7 Edge units that were introduced last month. That said, Kantar found only 9% of Samsung's users were using the then-current-gen Galaxy S6 iteration.

The Galaxy S5 outperformed the Galaxy S6
Instead, Kantar found a plurality of those upgrading, 26.2%, were choosing the Galaxy S5. The Galaxy S6 represented a departure from prior versions, with the device looking more like Apple's iPhone line. Samsung's phone reboot lost a few features Galaxy fans had come to expect, including waterproof design, a micro-SD slot, and a swappable battery.

Consumer Reports responded by rating the newer phone lower than the prior Galaxy S5 iteration. The newer Galaxy S7 brought back the waterproof feature and the micro-SD slot and increased the S7's battery capacity nearly 20% to make up for the swappable-battery feature. That may boost upgrades in high-end developed markets and increase upgrades.

Apple's Cook has been upfront with his desire to increase its market share through "Android switchers." The iPhone SE is considered a gateway phone by many analysts to introduce many mid-range customers to Apple's ecosystem. If anything, Apple's newest phone should increase its upgrade percentage from those who prefer a smaller phone. Will this help Apple grow unit shipments over Gartner's 7% figure? While that's not totally clear, Apple's new device further puts pressure on a company that sold more off-gen Galaxy S5 units than high-end Galaxy S6 units. Samsung has been aggressive to compete with Apple on the extreme high end but may want to put more marketing money behind a solid mid-range unit to mitigate the iPhone SE's risk.