LUKS does the key management (it's the Linux Unified Key Setup), dm-crypt performs the encryption and can use various ciphers, AES is the cipher. As long dm-crypt implements AES correctly, it should not be less safe than other programs that use AES-256. On the other hand, a company named ElcomSoft released a program last year that steals encryption keys from RAM for TrueCrypt, PGP, and BitLocker encrypted containers, but not for LUKS/dm-crypt encrypted containers, so LUKS/dm-crypt is safer than those other programs, at least in that regard. http://thenextweb.com/insider/2012/12/20/this-299-tool-is-reportedly-capable-of-cracking-bitlocker-pgp-and-truecrypt-disks-in-real-time/