We have a similar workflow that we use in the WisDOT Bureau of Aeronautics. Did you define the elevation of each vertex in your polygon? It should be in the same vertical units as your LAS data and map projection/coordinate system. The result is viewed as a Scene.
If you have access to the Esri Airports Extension, then you might be able to use that to analyze the obstructions as well. If you don't have the Airports extension, you could try converting all your data to raster surfaces and perform a raster analysis to compare the heights. Th raster solution is a little more complicated.