As matrix is federated, every user can be on their own homeserver, which will be storing a copy of all messages seen by that user.
E2E is more recent and optional. Most rooms are not E2E, and have browsable history.
Signal: Only E2E, with clients themselves storing the only copy of messages. You can only see messages that a device has received.
Any app you did not write/review and compile requires trusting the author, so this is not a signal specific concern. A crypto app can always store and send keys to a server if it wanted.
However, unlike WhatsApp, these apps are open source and can be reviewed and compiled if you so desire.
E2E is actually turned on by default, as of about one year ago.
Not sure how this is meaningful especially without further context. A large number of rooms on matrix are public channels to begin with (eg bridged rooms from irc, open source collaboration channels, etc), so they have no need for e2e encryption. All this is really saying is that E2EE is optional, which you already said (and which I'd also argue is probably irrelevant, especially given that E2EE is on by default).
Worth noting that Matrix's crypto is also based on Signal's algorithm (but extended to support efficient encryption in rooms with a large number of participants).
I was confused since the tone of that sentence sounded weird (Apart from <positive>, it also <negative>), but I think it's a typo - I believe you meant to type "Apart from Telegram not having E2E encryption by default"?
Signal's double ratchet algorithm is easily the gold standard for now and there's little reason for anyone pushing a E2EE privacy narrative to not be using it.
And I hate that Signal's identity is linked to a phone number.
You say that, but for a number of my contacts this is a significant hurdle... especially relatives.
people get that done - look at Instagram which grew despite having to do the exact same
I run my own server and don't need my message history to live forever there.
I also have mine set up though without a default_policy so I can have the server forget stuff in my bot control rooms cause they get cluttered with useless stuff pretty fast.
Signal works with a contact list, for private 1 to 1 and private groups. You need a phone number to use it, and they claim to encrypt almost all metadata, such as message senders. Signal claims they cannot read the content nor the history of users actions (but you have to trust them on that, they claim to use SGX enclave stuff, but can anyone technically verify that they do what they say they are doing?)
Element works with rooms, there is no contact list. A 1 to 1 conversation is a room with 2 people. The homeserver Matrix.org stores all metadata and they are readable (metadata are not private/not encrypted) by Matrix for some features to work. You only need a nickname to use it (at least for now). The content of conversations are e2e encrypted. In theory, i understand it would be possible for a matrix server to delete any metadata/messages once messages are delivered, but some features would not work, and you would also have to trust the server to actually delete the metadata.
Would be happy to read anyone who could correct or complete me.