In general the different distributions are very similar, and the main differences beyond the package-management tools is the configuration of particular software.
For example under a Redhat / CentOS system you'll install Apache via rpm and the configuration files will live beneath /etc/httpd. Under a Debian/Ubuntu system you'd install via apt-get and find that the configuration files live beneath /etc/apache2.
This is a trivial example of both systems running the same software, but it being slightly different. In real terms though the differences are trivial.
Perhaps more interesting are the different systems chosen by the distributions. For example the mail-server installed by default would be sendmail on CentOS, postfix on Ubuntu and exim4 on Debian. These choices can usually be changed, but you might find yourself struggling to replace larger and more core components such as the startup tool (upstart vs sysv-init etc).
Update: /proc & /dev will be largely identical across systems running a given kernel - as they come from the kernel (+/- udev/upstart).