It sounds as if you're confusing the purpose of the browser windows. Basically, you've got:
MXM Browser:
- just used for browsing MXM files on your disk, so you can drag them into the scene. Optionally, you can start up MXED directly from here through the right-click menu, though I figure this would rarely be used. Nothing is supposed to happen if you double click a MXM file in this window.
Scene Materials Browser:
- shows the plugin Materials currently contained in the scene. The right-click menu in this browser has lots of functionality, and double-clicking a Material here will show the plugin's Material Editor, just as it did in previous versions.
These pretty much work exactly as they did in 1.5.1, they're just not housed in the same window as the Material Editor anymore. This actually is how it was in the first version of the plugin, and I got quite a bit of feedback wishing that the plugin could once again use separate dockable windows - that's what they originally were before I put them in tabs in the Material Editor in 1.5.1. So, you can run them now either as standalone windows, or as docking windows - in Plugin Options > Display Options you can control whether each of the windows is standalone or dockable. Here's a screenshot from the help files which shows the Scene Manager and Scene Materials Browser both docked to the right of the screen, which happens to be how I use them:
I run the MXM Browser as a normal window, and it's hardly ever opened - mostly I create Materials from scratch, by using the plugin's Material Wizard, or by importing a previously-saved Material Library. I'm sorry if you preferred it when the browsers were in the same window as the Material Editor, but I don't suspect I'll be moving back in that direction again.
JD