The concern is over the artificial sweeteners in the diet drinks. There are anecdotal reports of neurological conditions such as memory loss, brain tumors, and seizures. However, I was not able to find any evidence in the medical literature that would substantiate any of these claims.
The consensus is that since obesity, diabetes, and heart disease are so prevalent in our society there is more benefit in reducing the total calorie intake by drinking diet sodas rather than regular sodas. In summary water is better than diet soda which is better than regular soda. And like every thing else moderation is key.