"Wickr is light-years ahead of Snapchat and they have an entirely different philosophy," said Chris Weber, a co-founder of Casaba Security, a firm that specializes in helping companies keep their networks secure from hackers. "They are all about secure and private messaging with this extra feature of self-destruction," he said.
Even metadata, which is data that include how or when a message was collected, is completely erased with Wickr's shredding feature. In other words, Wickr forensically scrubs or "shreds" the details about a message from your device so that there is no evidence the message ever existed.
Hackers and security experts have also repeatedly said that pictures and videos shared via Snapchat are not completely erased from a user's phone after viewing.
"With Snapchat, the idea and concept is exactly right-on. But making data self-destruct is very difficult and takes constant diligence. So people think their data is disappearing on that app, but it's not in a lot of ways," Sell said.
(Read more: Snapchat apologizes for security breach, updates app settings)
Messages sent via Snapchat are vulnerable because they are unencrypted and saved on a server until the recipients view the message, Weber said. In fact, unviewed messages are saved on Snapchat's servers for up to 30 days, according to the company's website.
CNBC reached out to Snapchat for comment about its security procedures, but the company declined to comment stating that it is "currently not participating in any media opportunities."
One reason Snapchat likely hasn't taken more measures to secure its messages is because the company wants to keep—and make money off—a small selected portion of your data, Sell said. (Companies like Google and Facebook, of course, use customers' information to sell targeted ads.)
Wickr doesn't plan to make money this way, but instead plans to sell premium services, like encrypted phone services—to make money, Sell said.
"Private correspondence is a basic human right and it's something we want to bring to the entire world," Sell said. "The idea is that we want millions and billions of people to use our free service, but the top 3 percent will pay for specialty features like international calling and conference calling."
"What we always say is we need to offer a secure service with cool features that are better than our competitors' (features)," she said. "We treat users well and don't trick them. It's the loyalty factor."
—By CNBC's Cadie Thompson. Follow her on Twitter @CadieThompson.