Depends on what you mean by “secure”, being very loose with the definitions, we have

• end to end confidentiality (i.e. only you and the intended destination can see the message contents)
• privacy (only the destination knows i’m sending messages to them)
• anonymity (no one can find out who you are, where you live, i.e. metadata/identity/etc)

My personal preference is Simplex.

Reasoning for a few:

• Email: even if you use PGP to encrypt messages the server(s) in the delivery path have access to all metadata (sender, receiver, etc, etc). If no encryption is in use, they see everything. Encryption protocols in e-mail only protect the communication between client and server (or hop by hop for server to server)
• XMPP: similar reasoning to email. i.e. the server knows what you send to who. I should note that XMPP has more options for confidentiality of message content (PGP, OMEMO, others). So I find it preferable to email - but architecturally not too different.
• IRC: Again similar reasoning to email - even if your IRC server supports TLS, there is no end to end encryption to protect message contents. There were some solutions for message encryption/signing, but I’ve never seen them in the wild.
• Signal: Good protocol (privacy, confidentiality, etc). Dependency on phone number is a privacy concern for me. I think there are 3rd party servers/apps without the use of phone numbers.
• Simplex: Probably the strongest privacy protection you can find, but definitely not easy in terms of usability. The assumption is that we do not trust the intermediate server at all (and expose nothing to it), we just leave our encrypted messages there for the receiver to pick up later. It also does some funny stuff like padding messages with garbage.
• Matrix: In theory it supports end to end encryption in various scenarios, but my experience with it has been so bad (UX, broken encrypted sessions) I only use it for public groups.

Some more food for though though; these protocols support both group communication and 1-1 messaging - privacy expectations for these two are very different. For example I don’t care too much about confidentiality in a group chat if there are 3000 people in there. It might be more concerned with concealing my phone/name/metadata.

In general I consider large group chats “public”, I can try to be anonymous, but have no other expectations. e.g. some people use some protocols over ToR because they do not trust the service (or even the destination) but they try to protect their anonymity.

On a technical note: I don’t think there is any protocol that supports multi-device without some kind of vulnerability in the past. So I would temper my expectations if using these protocols across devices.

I’m not familiar with the other ones that were mentioned in comments or in the spreadsheet.

I’d go with Signal or Threema

Signal: Best data protection. They are on a different level from anyone else. They even reimplemented gif search through their app so it can be anonymised (instead of the data-collecting gif search in your keyboard). Just an example, they really try. Also has a desktop app that doesn’t need the mobile app to be running. Downsides are google dependency (for push notifications - but they’re empty, the encrypted data does never even touch google) and required linking to phone numbers. They do have usernames now so you don’t have to give out your phone number to talk to someone. Behind it is an US based non profit - whether that is a downside everyone can decide for themselves.

Threema: No need for phone number, not even a credit card, you can buy it anonymously through their website. No google services required. Swiss based company, so much better laws than USA. Finance themselves through the one time fee of 2 USD and through their corporate offers, no nags for donations, no selling of data. Downsides are server code is not open source, and their protocol is less good than Signals, but still reasonably secure. They’re working on a new one though. Also no independent desktop app yet (also working on it).

Email, probably. Kind of depends on your needs, and how willing other people are to accommodate them. The most secure messaging platform is email with a third party IMAP client using OpenPGP. That way the client and the server are run by different people, and the encryption is based on a verifiable and well known standard. But will other people use that to communicate with you? Probably not. So probably something like Signal would strike a good balance between privacy and ease of use.