I recently upgraded from LR4. I never had issues switching between catalogs in LR4. With LRCC, I can select a recent catalog, but NOTHING happens. It just stays on the current catalog. I can also direct LR to open a catalog, but again, NOTHING happens. The only way for me to get to a different catalog is to shut down LR and go into my HD to find the other catalog I want to open. Why isn't it working anymore??? It is so frustrating!
For Lightroom to 'switch' catalogs. it has to close one catalog and re-start with another.
You can see a list of catalogs to choose when you start Lightroom by holding down the ALT key as Lightroom loads.
You can also set preferences to show the catalog selection screen when Lightroom loads.
In your situation-
Maybe you will have to manually load each (LR4) catalog (by opening the LR4xxx.LRCAT file in LR6) to convert it to the LR6 format, so as to be recognized by Lightroom-6 in future.