WhatsApp doesn't store messages on their servers, which is one of those features I really like in a privacy point of view. Signal does the same, its web app only loads the messages from your phone and they are not stored to any servers.
Doesn't that mean you can't carry on a conversation on another device?
It seems that was the main reason people didn't like Jabber to start with.
Whatsapp makes you to stay connected at the same time on your phone to use their web/desktop apps.