Mr Zuckerberg posted a photo on Facebook and Instagram of a WhatsApp billboard that shows the limitations of the iPhone, with a green bubble appearing for Android users and a blue bubble for iPhone users.
“WhatsApp is far more private and secure than iMessage, with end-to-end encryption that works across both iPhones and Android, including group chats,” Mr Zuckerberg claimed in the post.
“With WhatsApp, you can also set all new chats to disappear with the tap of a button. And last year, we introduced end-to-end encrypted backups, too. All of which iMessage still doesn't have.”
Some users have encountered problems with cross-device messaging, compressed videos and other issues.
Google earlier this year slammed Apple, saying that its technology turns texts between iPhone and Android users into “SMS and MMS, out-of-date technologies from the 90s and 00s”.
The tech company says Apple should use Rich Communication Services, which it calls the “modern industry standard for messaging”.
“These problems exist because Apple refuses to adopt modern texting standards when people with iPhones and Android phones text each other,” Google says on its website.
As part of its campaign, Google used a song from Canadian rapper Drake in an “unofficial lyric explainer” to discuss the problem with the green text bubbles.
Facebook acquired WhatsApp in 2014 for $22 billion.