I own both the CM cup holder and the tag-a-long from Chatterbox. Like piratesmate wrote, the tag-a-long accommodates the larger mugs. The opening for the trash bag is also larger on the tag-a-long.
Tip for those that own the tag-a-long: I always struggled with how to attach one of the plastic grocery bags for the trash. A friend started using those little metal clips that you can buy in the office supply section...they work perfectly!