Below you can see the front view size comparison of Canon 1D MII N and Canon 1D MIII.
Weight is another important factor especially when deciding on a camera that you want to carry with you all day.
Canon 1D MIII is significantly lighter (230g ) than the Canon 1D MII N which may become a big advantage especially on long walking trips.
Also keep in mind that body weight is not the only deciding factor when comparing two interchangeable camera bodies, you have to also take into account the lenses that you will be using with these bodies. Since both Canon 1D MII N and Canon 1D MIII have the same APS-H sized sensor, their lenses for a similar focal length and aperture will be similar in size and weight.