There seem to plenty of resources out there to help users of CAD software move to using desktop GIS but is the reverse also true.
Ok well a major difference you will find is CAD is geared towards a much more precise world. It supports more types of engineering based geometries and workflows to support dedicated workflows. The two industry leading CAD packages (Bentley and Autodesk) are easily as powerful as ESRI GIS but also tend to have a much stronger toolbox built behind them to facilitate large complex datasets.
Autodesk provides you native support to Oracle Spatial, no need for a ArcSDE. You also have powerful tools designed for business specific areas, versus just a vertical kit like Spatial Analyst or 3D Analyst.
Bentley provides a very competative toolset to Autodesk; but I was a Autodesk person first and that is where I fall back easiest, the command line tools of AutoCAD make eyes up work very smooth and easy to learn. Type 'Line' or 'Circle' and you get that tool, no hunting through toolbars or starting edit sessions.
Fundementally the biggest difference is that CAD is intended for production work, creating large volumes of high-precision complex data, less about cartography and pretty map output. In the end both of these CAD packages can created very good, complex outputs that easily rival ESRI, but they are different.
If you are talking about migrating data, then FME could definitely help you out.
There are a several tools I would suggest. Depending on what brand of CAD will be the preferred software.
If Autodesk is in the mix then I strongly suggest autodesk map3d. If civil engineering is the industry then civil3d has map in it also (along with many engineering tools).
As you have noted the migration path you are suggesting is not the norm.
In the case that you are not nessecarily talking about removing GIS but simply integrating the workflow between GIS and Cad. Here is a useful white paper on the subject... Removing obsatcles
IMHO GIS has great tools for managing data, while CAD has great advantages (slowly being met with GIS) in creating data.
Finding ways to utilize the data in both has been my theme for many years now. There are avenues to accomplish this through Postgis, SDE, Oracle.
It is important to think hard about the workflow and spend time answering user concenrs.
In my experience if it isn't fast, easy, and doesn't help greatly they just won't use it as designed.
Consider this reversed workflow.
Also ESRI has Arcgis for Autocad which has been improved lately and can accomplish some of the same functionality from the ESRI point of view. Which is slightly different from my POV but more and more workable with new technology.
In fact you can now consume arcgis server map services in the ESRI autocad client (you have had the capability of consuming wms in map3d for some time).
I use GlobalMapper to migrate GIS data (shp) to dwg, dwg to shape, kmz and many other vector data.
It works well.