The only thing that gets transferred when importing a route on a nuvi is the start point, destination, and any explicitly set via points. Shaping points (soft vias) are not sent. The nuvi will recalculate the route on import using these points with its own map and routing preferences.
In Mapquest, you need to convert all the via points to "stops" before you send the file to the nuvi. Right click on each via point and on the pop-up menu select "Make this point a stop".