The index of refraction parameter is for Fresnel reflection, whereas chrome is different. Chrome reflects light uniformly in all directions, but you can approximate that by using very high indices of refraction. 20 or 30 are high enough to get nearly uniform reflection.
The first image probably looks more like what you expect just because it is brighter. But the reflections are brighter than the sky it's reflecting, which is impossible. So really what you need to do is make the sky brighter, not make the object more reflective.
Matt