The Signal messenger and protocol.

I'd be cautious of Beeper. I guess my biggest concern personally is that it introduces an unnecessary middle man, and its closed source and proprietary, so there's no way at all to verify any claims they make.

To be charitable, I do think their claim on re-encryption of messages through the services themselves is true, but I think the bigger concern here is that whatever messages you send/receive also go through Beeper and not only services like Signal/iMessage/WhatsApp, and I'm unsure if Beeper encrypts the data they receive, or what access they have to it/how they handle it. That's my biggest issue, as it would effectively make end to end encryption on these services useless if Beeper just had full access and could see all of your messages and any metadata, which is what I suspect is the case.