One difference is that while broadway only works with GTK programs, Greenfield theoretically should work with any Wayland-supporting program (including apps using GTK 3 or 4). I wonder what options there are for running an X11 server in a browser..

> I wonder what options there are for running an X11 server in a browser..

Xpra can do something like that, or you can run a headless X server with x11vnc, or just Xvnc, and then front it with Apache Guacamole or such.

There was an X initiative, also called Broadway, to remote X applications over relatively slow internet links. I seem to recall a browser plugin X server as part of this.

Wasn't getting rid of the network transparency the proclaimed reason to switch from X to Wayland?

No, not at all. It was just a FUD argument.