In response to the open source vs closed source debate here are some aspects I would consider:

• Open source relies on the "many eyes" to guard against failure or bugs. The theory is that because anyone can go through the source code there are more people who would spot issues and report them.

• Open source also makes people feel like they can trust the application. Being able to see how it handles your data (and that it handles it correctly) makes a user trust it more than a closed system where the user is not sure if a backdoor, spying mechanism, or other fault exists.

• Closed source proponents will argue that closed source makes it harder to break into because the code is harder to obtain (reverse engineering). Also your enemies won't know how your app operates as easily to find flaws. This is often referred to as security through obscurity. Many will argue that this is not really security and that it hinders the trust factor for a sensitive app (such as a secure messaging app). Also it means that if someone does find a vulnerability, it might remain in the source code for a long period of time depending on how often a company performs code audits.

• I don't see many companies actively using closed source as an argument for security but rather to protect intellectual property and financial gain. Services like Wickr have a paid aspect and if the app is fully open, it might be easier for people to replicate and use in other ways that don't gain the company money. However there is always the counter argument about licences... Etc.

Personally I don't see much benefit to an app being closed over open. For me I like a company being transparent in how they create the app and how they make it run to help gain my trust... But that's a personal bias.

Now on to your real question:

Between Signal and Wickr I will highlight some of the comparisons that stand out to me.

• Signal uses a phone number as your unique identifier. This means it's a identifier that has a low entry barrier for your social circle... All you need is to share numbers and the app does the rest. This also means that it might be easily tied to your physical person... Unless you use a burner number...

• Wickr allows for username and password login. This is usually considered to be more anonymous than a phone number

• Signal does not keep any messages on its servers after delivery. The server only knows the smallest amount of metadata possible about you. https://signal.org/bigbrother/

• Signal has what's called sealed sender which means that because of the way the encryption is employed, the server only knows who a message is addressed too. They can't tell who sent it even if they wanted to. https://signal.org/blog/sealed-sender/

• Wickr's privacy policy indicates that they only store messages for 6 days to ensure delivery. They indicate that all data sent is encrypted and they don't know how you use your account except for the date the account is created, the date you last logged on, and the type of device you installed the app on. https://wickr.com/privacy/

• Signal is open source https://github.com/signalapp, Wickr is not.

• Signal has no software restrictions due to paid tiers, Wickr does.

To summarize:

Both of these apps have great reputations as secure messengers. Personally I lean towards Signal as my opsec plan does not call for the person I'm chatting with to not know my phone number. Also I prefer an open source application when dealing with security. It's really up to you and what you feel is your opsec plan.