NEVER shy about hype, on September 12th Apple’s boss, Tim Cook, presented the firm’s latest iPhones to a packed auditorium in its glitzy new headquarters in Cupertino. He made a grand prediction: its new, premium phone, the iPhone X (pronounced “ten”), will “set the path of technology for the next decade”. Set to be released this November, ten years after the first iPhone launched, the iPhone X has new features such as an edge-to-edge OLED screen (a thinner screen that does not use a backlight), wireless charging, facial-recognition technology and a dual-lens camera.

On the same day, Samsung, a rival smartphone-maker, held a lower-key event in Seoul. Koh Dong-jin, president of Samsung Electronics’ mobile business, announced that next year Samsung could reimagine the smartphone entirely and launch a new design with a foldable screen, which can close like a small book. On September 15th its latest premium smartphone, the Galaxy Note 8, will go on sale, boasting many of the features offered by the iPhone X.

Both are trying to convince consumers to spend around $1,000 for their new gadgets. Samsung’s new phone will cost $960; Apple’s high-end iPhone X will cost $999, 45% more than the average selling price of an iPhone in 2016. (The iPhone 8, simpler than the X and available for sale in September, will start at $699.)

The competition to wow consumers has been intensely fought between Apple and Samsung Electronics for years. They claim a duopoly over the premium part of the smartphone market. Together they control around two-thirds of the global market (Apple claims 44% of smartphone revenues and Samsung 22%; see chart). The two firms have tussled in courts around the world over intellectual property, with Apple accusing Samsung of infringing on its smartphone patents. Last year Apple seized share in premium phones when Samsung struggled with its Galaxy Note 7; its batteries had a habit of overheating, which necessitated a global recall. Samsung’s new phone is expected to win back users. It used to copy Apple’s innovations but is now often ahead on new features, says Werner Goertz of Gartner. Samsung was the first to release an OLED screen, for instance. The rivalry between the two will only grow fiercer (even though Samsung is also among Apple’s most important suppliers of components, and is expected to provide OLED screens and chips for Apple’s latest phones). In rich countries the market for smartphones is maturing: many of the firms’ gains will come from stealing each other’s customers. In emerging markets, especially China, they will compete to persuade consumers to trade up from cheaper phones. Apple globally claims an 82% retention rate, compared with Samsung’s 67%. This is significantly higher than other firms’, especially Chinese manufacturers like Xiaomi and OPPO, whose less expensive phones have gained share among Chinese consumers in recent years. Samsung and Apple will fight on three fronts. One is to design a better overall software ecosystem and keep consumers within it. “I don’t know if it’s a smartphone war as much as it is an ecosystem war,” says Tim Bajarin of Creative Strategies, a technology consultancy. Samsung runs on the Android operating system, whose design it does not fully control, whereas Apple has the advantage of complete oversight of its iOS operating system.

A second front will be fought over virtual assistants. Apple was the first mobile-phone maker to offer a voice-controlled assistant, called Siri, which it introduced in 2011. Samsung offers one named Bixby. Both have been underwhelming in their capabilities. But Samsung is investing huge sums to change this, while Apple is criticised for underinvesting in Siri.

A third battleground in software will be augmented reality (AR), or the projection of digital information onto the physical world. Both Apple and Samsung offer dual-lens cameras, which make it easier to integrate AR functions into apps.

There is unlikely to be one winner. Samsung is well hedged; its strong chip and smartphone-components business will insulate the firm if mobile-phone sales slow. Apple lacks this diversity, but its mobile devices project luxury, and its customers are less likely to defect because iOS runs across all their devices. Mr Cook may be right that Apple’s phones will set technology’s direction, but his firm will feel Samsung’s breath on its neck all the way.