You can use the Ethernet network in the manner to which you are accustomed. Any protocol that you can send over Ethernet, you can send over CobraNet. I can't think of a protocol that has not been made to pass over Ethernet. A computer is not necessary. But any computer with an Ethernet interface will do.
Ethernet is the more entrenched network.
Ethernet is evolving faster than IEEE1394 in terms of capabilities and bandwidth, and Ethernet is cheaper than IEEE1394. There is really only one type of CobraNet deployed today. Let's say I want to send QSControl II over the same wire as CobraNet. Ethernet allows for multiple protocols to coexist on the same wire. They do not interfere with each other.