LUKS is an on-disk format where as TrueCrypt is both an on-disk format and an application.zuluCrypt is only an application that supports multiple on-disk format

LUKS is an on-disk format where as TrueCrypt is both an on-disk format and an application.zuluCrypt is only an application that supports multiple on-disk formats so your question is not easy to answer since it mixes up different things. LUKS advantages over TrueCrypt is that it can support up to 8 different passwords and each password security can be fine tuned by a changeable pbkdf2 iteration count that is set per password. TrueCrypt on-disk format advantages over LUKS is that it can support two volumes(outer one and hidden one) and its header is completely hidden since its encrypted.LUKS volume header is unencrypted and hence visible. With a LUKS based encrypted volume,its possible to mimic a hidden header on a device through the usage of a "detached header" but this is a property of tools that manage LUKS volumes and not of a LUKS volume on disk-format.It is also possible to mimic a hidden volume through a plain dm-crypt volume at a non zero offset but this is also a property of a tool that manages LUKS volume and not of a LUKS volume format. When it comes to binary applications,zuluCrypt is better than TrueCrypt because it supports TrueCrypt on-disk format together with other formats and it also supports multiple hidden volumes through the use of plain dm-crypt volumes. zuluCrypt also supports LUKS volumes with a detached header and this is more or less like TrueCrypt volume that requires a password and a keyfile(the detached header will act as a keyfile in this case). zuluCrypt also supports plain dm-crypt volumes at a none zero offset and this means it can have more than one "hidden volumes" although it does not offer protection of these hidden volumes.