Apple (NASDAQ:AAPL) and Samsung (OTC:SSNLF) are unquestionably the top smartphone vendors worldwide, but when it comes to specific markets smaller competitors can pressure the tech giants. That's exactly what's starting to happen across Europe and China, as cheaper devices are making gains against the higher-end Apple and Samsung smartphones.

Changing China's market
The latest Kantar Worldpanel data illustrates the gains being made by smaller vendors in these marketsChinese smartphone vendor Xiaomi outsold Samsung devices in China in March and April. Kantar said the Xiaomi RedMi smartphone was the top-selling smartphone ithe world's largest smartphone market -- and 23% of those who purchased the device were former Samsung customers.

Xiaomi isn't just coming after Samsung. In the first quarter of 2014, the company held the No. 3 smartphone vendor spot behind Samsung and Lenovo -- leaving Apple as No. 4. As far as operating systems go, Apple's iOS is falling behind as well. In April 2013, Apple's iOS held 23.7% operating system market share in China, but that fell to 17.5% last month.

Screenshot of changing OS market share in China. Source: Kantar Worldpanel.

Losing European euphoria
A similar situation is building in Europe, as China's Xiaomi and local European vendors introduce cheap smartphone devices into the market.

Here's what Dominic Sunnebo, Kantar Worldpanel's strategic insight director, said in the report: "Across Europe there is an accelerating trend of fragmentation in the handset market as smaller brands gain real traction. Established brands like Motorola and Sony are showing resurgence and newcomers to the European market such as Huawei and Wiko are challenging the established names."

Sunnebo mentioned that as subsidies have been separated from smartphones in some markets consumers are realizing the real cost of their devices, and some are opting for cheaper ones. That's one reason Huawei saw smartphone sales spike 123% across the U.K., Germany, France, Italy, and Spain over the past year.

While the smartphone OS market share has somewhat stabilized in Europe, Apple's iOS comes in at No. 2 with just 17.5% share, while Android takes an overwhelming 72.4%.

Foolish thoughts
The rise of companies such as Xiaomi in China shows that Samsung and Apple don't enjoy the same influence that they do in the U.S. While the two are clearly strong brands worldwide, this latest Kantar Worldpanel data show just how fragile their positions in large markets such as China and Europe can be. Small French smartphone maker Wiko recently took 8% market share in its home country and has plans to expand into other parts of continental Europe and the U.K. That many not seem like a big deal now, but adding its share to other smaller vendors starts putting a real dent in Samsung and Apple devices.

Samsung's advantage is that it does a good job of diversifying its product lineup across a wide range of device and prices. Apple, meanwhile, sells its iPhones for high premiums; even older devices like the 4s sell for several hundred dollars, unsubsidized. While Apple wants to continue down the premium-brand path, that strategy may not pay off in all markets over the long term.

Apple could easily sell older devices at cheaper prices if it chose. This would allow the company to keep its premium status while grabbing share in lower-priced markets. Apple has not yet made such a move, but if China and Europe continue moving in the direction they're going, this tech giant may not have a choice.