You might want to check with a podiatrist about what kind of sole you need. I know this is different than arthritis, but a friend of mine has been having some nerve problems in one of her feet. They removed the nerve, but she's still having a lot of pain months later. Her doctor said she needs to give up her carbon soles, because they are too stiff and aggravating her problems. She's also getting custom orthotics.

So, for efficient power transfer, stability, and comfort the lightest, stiffest shoe is best. For specific medical problems, though, it could depend. A stiff sole may support your painful joints better, but you may just need the right insert.