I've worked on many veterinary projects in my career. Along the way I learned that dogs prefer a grippier surface to a flatter smoother surface. In fact, during one project with our local animal control department I learned that when being tested for aggression, dogs will more often test positive when the testing is conducted on slicker flooring surfaces such as vinyl. As a result they chose to use rubber flooring in certain areas of the facility.
What I was told by the docs involved was that when the dog doesn't feel secure in its footing it develops an aggressive defensive posture and during the testing for aggression this can translate to a more aggressive test result.
I think the challenge you would have with rubber in a home, depending on your decor, would be finding something that didn't look too institutional.
Another good alternative would be cork. My own preference in cork is to have the cork mounted on a backing system. There's a company called Wicanders who does a nice job with this format. I also found it incredibly scratch resistant. I actually took a car key to some and couldn't really damage it.
I wish you the best with your project and hope you find the perfect solution.
