I'm going to start with a quick history lesson. Cisco originally made routers. At some point in the 90's (not sure of year) they bought a company called Catalyst that made switches, putting Cisco into the switching market. Cisco routers at the time were running Internetwork Operating System (IOS), generally the command shell that people think of nowadays when they think of Cisco. Catalyst switches ran their own OS called CatOS. Lately, Cisco has been transitioning those switches from CatOS to IOS, which makes sense, because that's one less thing you'll have to learn with Cisco.
Some people are of the opinion that CatOS is faster to configure than IOS. One reason, is that you can configure with CatOS without going into config mode with the "set" command. Other router/switch manufacturers have their own OS or firmware for their products. Juniper has JunOS, Extreme has XOS, Enterasys has at least four or five different shells or menu-based firmwares. For me, it doesn't really matter how the shell or GUI or whatever they use is set up, just as long as you know the principles, you can configure most anything. It's just learning the interface.
As far as the internal workings of each OS, that isn't something that the companies disclose much of. XOS is apparently the only company that has a switch/router OS that is modular, but Cisco is working on that with it's IOS. So, the differences that most administrators have to worry about is features supported, and the interface (shell, etc.) it uses.
-Jeremy-
