The Core Systems are the same, but the Design Version is targeted for working with CAD data.It has some better interoperability with AutoCAD, Civil 3D and other Autodesk products.
It also has some better lightning simulation and analysis tools which are more suited for architect and civil engineers.
This applies to only to versions prior to 2016.
Note: 3DS max 2016 is the only version, there is no longer a "design" version.