WinRAR password-protected files are encrypted with military-grade protection. They essentially cannot be cracked by brute-force attacks, and you do not need to worry about third parties seeing these files. All of that hinges on the password itself being sufficiently strong, which is not something WinRAR controls.
WinZip password-protected files are extremely secure. They use military-grade encryption that is very unlikely to ever be cracked by a direct attack. As long as the password used to protect the files is secure, the WinZip security methods are robust and reliable for consumer and industrial use alike.
LUKS is very secure as far as encryption options go. It can encrypt an entire disk, protecting all of your data on a device, if you set it up that way. The biggest risk associated with LUKS is that it uses a password to secure the encryption, so an easily-guessed password undermines the encryption security.