This seems like a big misunderstanding on your part, and I think the comparison doesn't make much sense because in general they serve different purposes:
Vertex shaders are executed once for every vertex in the geometry, and are used to modify or add new information to those vertices. For example, they can be used to slightly modify the position of the vertex, or calculate a light value for that vertex.
Pixel shaders on the other hand are executed once for every pixel/fragment that covers that geometry, and are used to determine what the final color for that fragment should be.
It might be true that pixel shaders are used a lot more than vertex shaders, but that's because there are a lot of effects that require that extra control over the color of each fragment that are only possible with pixel shaders, e.g. things such as bump mapping, or any full screen post processing effect. Vertex shaders have different uses, and are used mostly for other types of effects such as creating waves in the ocean, and other types of distortions.
As for your performance question, if you can implement the exact same effect, with same visual quality either on vertex shader or pixel shader, then I think the vertex shader version will probably be a lot faster, because the number of vertices will usually (always?) be a lot smaller than the number of pixels covered by the primitive.