Construction History, PolyNURBS, and real geometry are the three main points. All models made in Evolve can be used directly for manufacturing since it is actual surface and solid geometry rather than polygonal. Complete history gives the flexibility to edit/update features, dimensions, etc...without having to manually rebuild models. With PolyNURBS tools you have basically the same workflow and ease of concept modeling you find in products like 3d Max, but the big difference is that your models are NURBS based, can be used directly to create molds, tooling....and can be combine with traditional surface and solid modeling tools for increased control and precision modeling if needed. And obviously you have integrated rendering so no loss in visualization.
Without knowing the companies process for producing products I can only assume they are sending out 3d Max models to be recreated in a CAD package in order to create models suitable for manufacturing. In this case there is usually some design elements that get lost in translation or inaccurately interpreted. By switching to Evolve it would give them more control over the products they are creating and also save them money in time and services needed for CAD support. Again this is all based on many assumptions.
If you end up going with this company and are having difficulty convincing them to use Evolve you can contact me directly at email@example.com. I'm sure we can arrange something to convince them and allow you to continue using Evolve.