GnuPG (Gnu Privacy Guard) is an open-source free software security and privacy application designed to provide encryption, digital signing and authentication for data communications, as well as for storage and transmission of data. It is widely used for encryption and authentication of emails and other communications, as well as for digital signatures and verification of files. GnuPG uses a variety of cryptographic algorithms, including the popular Advanced Encryption Standard (AES) and the Rivest–Shamir–Adleman (RSA) algorithm. It also provides built-in support for public-key cryptography, as well as a range of key management options. In addition, GnuPG includes tools for working with OpenPGP (Pretty Good Privacy) compliant applications. GnuPG is available for Windows, Mac OS X, Linux, and other Unix-like operating systems.
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As far as I can see, Axcrypt is a file encryptor. But GnuPG (and PGP in general) is mainly oriented to email body encryption and signing: not just files and not just encryption. Also, Axcrypt is for Windows only.