The FAQ has a very cautious explanation of the whole process, pointing out every imaginable pitfall. Once you've done it, it's a five minute job on most standard installations.
http://openbsd.org/faq/upgrade53.html
The official recommendation is to boot the installation kernel and upgrade that way, but I've never had a problem doing a remote upgrade. It's always been entirely painless.
One could argue that it's not quite as simple as "apt-get dist-upgrade" but I like it better - the upgrade process is more explicit about not touching your config files. And since it's a BSD, the base system isn't packaged, so I'm not entirely sure how it would work (although FreeBSD does have freebsd-update now, so it's possible).
Contrary to that, most companies would never upgrade a linux system. My feeling is, the most used "upgrade" plan for debian is to not upgrade as long as possible and then do a full reinstall with a new version.