You probably have a normal problem. When you look at the model in med, does some of the polies look dark blue? If you do not know what normals is, a normal is the direction a poly faces. A poly is only visible from one side. Try setting the show normal setting in med. the green line is the driection your poly is facing. You might need to flip them by selecting the polies and clicking flip normal button, on the top-right bar. As for the many vertexes, that is your original model, and your moddeler should scale down on the polys. Actually poly count is more important. Thats how we measure detail.

Hope it helps.