Be aware that the catalogs are NOT compatible. When you upgrade to Classic, you get a new copy of the catalog, still pointing to the same images.
You cannot open this new catalog in LR6.
If you open the LR6 catalog in Classic, it makes YET ANOTHER new copy of the catalog, which can be really confusing.
What's really an issue is that changes you make to the LR6 catalog are not reflected in Classic and vice versa, but ARE reflected in the images themselves. So for example if you drag and drop an image from one folder to another in Classic's catalog, the image just goes missing in the LR6 catalog because it does not know it was moved.
Apologies if all this was obvious, but I've seen people make a real mess running two major versions at once, ending up with a dozen catalogs and changes littered all through them.