I ran some tests network rendering with the two faster computers, and discovered that in Bryce 6/Lightning 2 the host isn't used to render the scene.  Monitoring CPU usage showed the host at zero percent most of the time, with spikes up to 20%.  Definitely not the behavior of a machine performing a complex render.

If that's true, and there's no way to get the host to work on the render, then a two computer network would be slower due to network overhead.  Or did you mean two clients and one host (three computers total)?

And for further reference, the scene I'm working on is a still image.