Zuckerberg only said that WhatsApp will continue to operate independently of Facebook, so we'll have to see what changes it does and doesn't make.
From WhatsApp's help page: "WhatsApp communication between your phone and our server is fully encrypted. We do not store your chat history on our servers. Once delivered successfully to your phone, chat messages are removed from our system." While WhatsApp doesn't save the content, it is stored on the phones your contacts use. That's a big difference between it and Snapchat -- once you view Snapchats, they disappear from your phone.