Still, the SMS is not dead and it is the go to choice for those who don't trust the application makers. That is specially the case of professional who need to exchange information quickly in their line of work.
The problem with text messages is that their common protocol does not provide sufficient protection for the its contents: the messages are sent in plain text, which means an eavesdropper could intercept what's being sent and received with relatively ease.
It's not a surprise that amidst so much concern with privacy and security that applications specialized in secure exchange of text messages exist.
One application that guarantees text messages can be exchanged security is Chat Safe. This free application utilizes strong asymmetric encryption to protect the contents of messages sent and received by anyone using the app.