Signal. Telegram is a business run by a millionare who is having fun. Signal is run by well known security expert / activist and his very transparent company Open Whisper systems.
The way Signal tackles the problems is smart gradual development and they are the closest to making the holy grail - e2e encryption without users even noticing it. There are no "secure" and "not secure" messages in signal - it is all encrypted and you can't turn it off. That's awesome.
Neither. Both require tying your identity to a phone number.
You're better off with Matrix/Riot or XMPP. Neither requires a phone number, both offer the ability to communicate securely, even with a compromised server. Both also support multiple devices, group chats and federation.
Signal periodically sends truncated cryptographically hashed phone numbers for contact discovery. Names are never transmitted, and the information is not stored on the servers. The server responds with the contacts that are Signal users and then immediately discards this information. Your phone now knows which of your contacts is a Signal user and notifies you if your contact just started using Signal.
However; I don't know if their server is peer-reviewed on a regulary basis, nor do i know if the software (besides the used ciphers) is also peer-reviewed. Can't find anything on it.
The way Signal tackles the problems is smart gradual development and they are the closest to making the holy grail - e2e encryption without users even noticing it. There are no "secure" and "not secure" messages in signal - it is all encrypted and you can't turn it off. That's awesome.