Hi Micha,
Moi3d is a Nurbs modeller. Nurbs usually show a very clean mesh.
When you export to 3ds (or obj or lwo and so on) you are converting the nurbs to polygons.
Polygons can look very nice as well, but detailed objects require many polygons which can make your model look messy.
Also, the more polygons you need, the larger the file, the more memory you need.
When you export using ngons, your model should look better. (playing with the export options can result in a cleaner mesh)

In short, your model, when exported using polygons, will never look like the one in your viewport which uses nurbs.

However, when you render the model it should, ofcourse, look nice and smooth again.