Ambos os comandos sobrescrevem dados usando padrões. O que usar em que situações certamente será uma questão de opinião, eu provavelmente rasgaria um arquivo e esfregaria um disco, mas como essa é apenas minha opinião, as seguintes informações podem ser úteis para você.
SHRED: Note that shred relies on a very important assumption: that the file system overwrites data in place. This is the tradi‐
tional way to do things, but many modern file system designs do not satisfy this assumption. The following are examples of file
systems on which shred is not effective, or is not guaranteed to be effective in all file system modes:
* log-structured or journaled file systems, such as those supplied with AIX and Solaris (and JFS, ReiserFS, XFS, Ext3, etc.)
* file systems that write redundant data and carry on even if some writes fail, such as RAID-based file systems
* file systems that make snapshots, such as Network Appliance's NFS server
* file systems that cache in temporary locations, such as NFS version 3 clients
* compressed file systems
In the case of ext3 file systems, the above disclaimer applies (and shred is thus of limited effectiveness) only in data=journal
mode, which journals file data in addition to just metadata. In both the data=ordered (default) and data=writeback modes, shred
works as usual. Ext3 journaling modes can be changed by adding the data=something option to the mount options for a particular file
system in the /etc/fstab file, as documented in the mount man page (man mount).
In addition, file system backups and remote mirrors may contain copies of the file that cannot be removed, and that will allow a
shredded file to be recovered later.
Fonte 'man shred'
Scrub:
Image Source: Centro de Software