Telegram uses their own encryption which may be a worry for some people as it hasn't been audited as much as something like the Signal protocol. Their source code isn't always up to date and their server is proprietary. End to end encryption isn't enabled by default and is only in secret chats. Secret chats aren't available on PC. Telegram only uses server to user encryption outside of secret chats which keeps the decryption keys on telegram's servers. That means they can decrypt the messages at any time they want to (unless using secret chat). You need a phone number to sign up which may not be wanted. There is a lot of misinformation about Telegram such as their encryption being proprietary but this is not true. Telegram has also used weak encryption in the past but this has been fixed with MTProto 2.
Threema is proprietary so we can not verify its protection. Threema can be used anonymously which is good but you should not rely on it for important conversations.
Signal is in my opinion the best encrypted messenger but it requires a phone number to sign up. This is to prevent spam from bots and to allow you to use the Signal app for SMS. Signal also doesn't allow third party clients or F-Droid builds. These are for security purposes so someone doesn't mess up building signal and compromising its security.