In the spline settings, try changing the Intermediate Points value to Adaptive and decrease the Angle value. For sharp curves use very low values. That should do the trick - both when working with Loft NURBS and HyperNURBS.
If you are using a rough polygonal model as a cage to fit inside a HyperNURBS model, you can as well increase the exactness of the fit by:
1) subdividing selected parts or the whole of the polygon model (Main menu - Functions - Subdivide)
and/or:
2) select vertices, edges or polys of the polygon model and use the Wight HyperNURBS tool on them (the exact procedure is described in the C4D Manual / Help, in the HyperNURBS section).