The 10 has a slightly larger brush, but lacks the adjustable double swivel joint that is on the 20. The 20 is more useful for tasks that require more flexibility and maneuverability.
Can you post a pic when you get it. I could use something bigger as well for my S7. As you said, that tiny little dot that they give you makes for a lot of work when dusting larger surfaces. I have at times resorted to using my parquet floor brush, but I'm not crazy about spreading floor germs on my coffee table and other furniture.