The context of the original post was discussing recovering plaintext when a bit of the ciphertext was corrupted - assuming you have the key and no backups.
In this case 'plain' dm-crypt results in typically 128-256 bits of plaintext not being recovered.
This guy has done some experiments and says in practice it's similar between corrupted encrypted and unencrypted data.
With LUKS, if the corruption is in the data, then the result should be the same as for dm-crypt.
But with LUKS, if the corruption is in the header, then there is a possibility *all* the data will be lost (again, we are talking of
with the key, but no backups). LUKS is actually designed to
maximise this possibility.
The logic is that an attacker is more likely to have a corrupted file. With a password based encryption sheme, the best proxy you have to an 'authorised' person is one who knows the password - in fact that's the only proxy you have.
So making it more difficult for people with the password to read the data, without making it more difficult for people without it to read the data, is a misfeature IMO.
An attacker maliciously changing the ciphertext to change the plaintext in a predictable way is another issue, but LUKS and dm-crypt are equally bad in this respect as neither support authenticated encryption modes.