Mac OS X Server basically has a GUI to configure all of the Unix tools under it, like apache, mail server, file sharing (samba), etc. Where Mac OS X Client has many of these tools, but no (easy) way to configure them (other than the terminal). And if you want to get recent, the latest 10.2.2 update enables journaling on the Server version, with speed optimizations (something client isn't optimized for -- yet).
Stability and Unix software/tools wise, they're both the same, just different to configure.