I understand you have some questions on the Compare Model extension in Revit. I'm assuming you are in 2015 as I don't believe the 2016 version is out yet. In any event see my comments below.
It seems like the primary dialog box is modal, in that it must be utilized for whatever command you want out of it, but you cannot leave it open and go back-and-forth between it and Revit.
Correct, you open the extension have it do something, then close it to continue working in Revit. You can save out the report and view it (Look under Reports after you do you comparison)
So if I want to select just the 'walls' that have changed, I must run the model compare tool, select the walls (which then exits the Compare dialog), now I want to select the 'rooms' that have changed, I must re-run the model compare tool?
Correct again, you can run the whole file, just a few categories or just one, but if you want to do something else you need to run it again.
It takes 15+ minutes to process my file each time the command is started.
How big is your file? When is the last time you ran Audit, Purged it three times and Saved as a New Central? This will help, but if the file is big it will take time to compare them. You might consider running the extension at the end of the day and saving off the results in the am. This way you would have to wait around for the results. Just don't forget to restart PC or at least Revit. I hope this helps and let me know if you have additional questions or comments.
Thanks for posting.
