first of all, dpkg --set-selections seems to accept multiline input on stdin (as per dpkg man page) – this is why it does not need xargs.
In the case of aptitude command, package names are added as command arguments; as there can be many packages, maximal command line length might be exceeded.
To avoid that, xargs is used: it feeds arguments (lines) from package_list to aptitude until the command line length limit is reached.
When that happens, another aptitude command will be constructed and run, until all lines from package_list are processed.

Sudo can be added either before xargs, or before aptitude – there should be no visible difference with default sudo configuration. I’d put sudo before xargs, though. I haven’t tested this, so please reply if your experience contradicts my advice

* I referenced this post @ http://unix.stackexchange.com/a/243510/38638

* I have a question about `sudo` and `xargs` in the package-restore commandline

xargs aptitude --schedule-only install < package_list; aptitude install

in a comment on the serverfault answer you cite.