Ill cover OpenBSD and Mac OS X since those are the only two Im adminning now (also use several other BSDs which I may comment on)
OpenBSD:
speed: Very fast, softupdates has helped io speed considerably and tcp speedups are in -current
stability: I have only had a few crashes. Most were because of a bad hard drive.
security: It all depends on the admin, just like any other system.
software compatibility: Its got a relatively small ports collection, which is mostly out of date (-stable).
harware compatability: Choose good hardware, it will be supported.
package management: ports is great. The only system that compares that I have used is Debian's apt-get
ease/power of install: It is the easiest, fastest install I have ever done. 20min on fast hardware, 30 for a net install.
quality of docs: Does any open source project have good documentation? No. But OpenBSD has the best I have seen.
recomended user level: newbie to power user. It all depends on if you really want to learn or not.
Mac OS X:
speed: The gui slows it down, but the overall system is quick.
stability: Its fairly new, but there is only so much hardware it supports so drivers are usually of high quality (on PPC anyhow, I havent used x86)
security: Apple needs to release patches quicker, but Im happy over all.
software: There is plenty of free software that works (think fink), and quite a few quality closed source applications that are worthwhile (omniweb)
harware compatability: It sucks on x86. The PPC version is quite nice.
package management: fink is a copy of apt-get basically. Its not standard though. Their .pkg system is ok, but not great.
ease/power of install: 1 maybe two clicks of the mouse.
quality of docs: Havent looked.
recomended user level: newbie - power user depending on what you want to do.
These are the only ones I feel like messing with for now, it would have been nice if this was included in my *nix thread