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..
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.