TextSecure is very open about the crypto protocol and provides details that independent researchers can evaluate. It's also made by a well-known expert that we trust to do it right.

Wickr is pretty shady about their protocol.

They also make me uneasy because they use the term "military-grade encryption" a couple times on their site. This is a pretty common snake-oil security term...so it makes me uneasy since the protocol details are nowhere to be found.