Publicly, Apple and Facebook have brawled over privacy issues, with Apple CEO Tim Cook and Facebook chief Mark Zuckerberg trading high-profile barbs over the past year. But behind the scenes the two companies are fighting what may be a more consequential battle for leadership in messaging, vying for customers’ attention and loyalty through Facebook’s Messenger and WhatsApp, and Apple iMessage.

That battle, which is playing out around the world, is now bubbling to the surface. The combined messaging presence of Facebook’s Messenger, WhatsApp and Instagram gives it worldwide sway. But in the U.S. and other valuable developed markets, Apple has a powerful presence.