Would a ct scan on the abdomen without contrast show kidney stones or gallbladder inflammation better than ultrasound?

Yes and no...: Non-contrast ct is superior to ultrasound for kidney stones, but ultrasound is actually a better study for gallstones and other gall bladder pathology than ct.

CT for stones: Ct without contrast is much better than us for kidney and ureter stones. Ct detects calcium better. Most gallbladder disease involves inflammation. Us is better for right upper quadrant pain and suspected gallbladder disease. It is also cheaper and involves no radiation, so it is arguably safer over a person's lifetime.