Apple's iMessage is secured end-to-end, your mobile carrier can't see the message. As soon as the box goes green then any intermediary, including your mobile carrier and your friend's mobile carrier, can read the message and/or make it available to law enforcement.

In a U.S. court of law Apple has stood up to authority and pointed out they can't provide the messages requested as they're locked even to Apple. Facebook on the other hand has acquiesced to U.S. law enforcement. That tells me that even if Facebook has secured end-to-end messaging, which I don't think they've ever claimed, they have backdoors.