Alan_the_coder I found an article from Wire saying that Element/Matrix isn't secure and doesn't always comply with privacy regulations.
Element is fine. The end-to-end encryption is correctly implemented and fully secure, and the project takes security issues seriously. Matrix home servers also need to comply with privacy regulations like anyone else, and does.
Element, Session and SimpleX are the only sensible options if you want anonymity towards the provider as well as those you chat with, while also having strong end-to-end encryption.
Some comparison to help you choose and understand implications:
Session and SimpleX are using cryptographic identities as handles, making sure the network cannot MITM attack your connection. Element and Signal do not inherently protect against these attacks, but require additional verification, for example by you and the one you chat with scanning each others QR codes IRL.
Session, SimpleX and Signal promises to delete your activity data from their servers, such as messages sent and so, after a certain time. Element on the other hand never deletes your data. It is still fully end-to-end encrypted though, so cannot be read by them or anyone else that can get access to the data.
Session, SimpleX and Signal are all trying to hide metadata about your communication from the network operators, such as information about who you chat with. Element is not hiding this metadata from the home servers. This might be an issue, especially if you are not anonymous to the network operator.
Session and SimpleX are allowing sign-ups without providing any information at all. Element is allowing sign-ups with only providing an e-mail address or invite code, which can still preserve your anonymity, as long as you connect through Tor or a VPN when signing up. Signal on the other hand requires proof of your identity for sign-up, typically through verifying your phone number.
SimpleX allows you to have a different pseudonym and handle per chat. Element and Session both also allows you to have an anonymous pseudonym, but it will be the same one for all your chats, so might mean somewhat higher risk of deanonymization of all your activity if one of your chats gets deanonymized. Signal has up to recently only allowed using your real identity as a handle, your phone number, and all participants in chats you are in would see it. They have recently added support for setting a pseudonym, but this is not the default behavior.
Element and Signal are driven as non-profits using donations alone, like most reputable security and privacy focused projects are. On the other hand, Session is tied to a cryptocurrency, and SimpleX have intentions to also implement a revenue making method into their network. Neither is necessarily better or worse than the other, but the implications of tying the network to a profit and financial incentive is not well understood.
As far as I know, none of the networks pad the file size of attachments, which might reveal their identity. But all networks end-to-end encrypt file attachments in a secure way too, like the rest of the chat.
Usage of voice and video calls may not preserve your anonymity or privacy. It is recommended to disable that if you need anonymity and privacy. I know Element and Signal fully end-to-end encrypts voice and video calls in a secure way, I am less certain about Session and SimpleX. I know at least Element and Signal leak your IP address to the other party by default, I don't know if Session and SimpleX also suffers from this issue. I know in Element and Signal you can change the settings to hide your IP address from the other party. Sharing the IP address is likely not an issue if you use a VPN anyway.