I think you will have to provide a little more explanation. There are multiple featureclasses in the 2 file geodatabases that you provided. From your screenshot I can derive that you want to update the fc COM_Box, but with which other featureclass? Is it InteriorSpace perhaps?
A thing to keep in mind is that the information has floors. So polygons overlap at the locations of the points and therefore a point will fall in multiple polygons and could receive multiple different ID's: See a 3D shot of a small part of the data. The black points have been extruded to show the effect and only the 1st to the 6th floor has been visualized:
Just had another look. Since both layers (if the ones I mentioned are the ones you mean) have a Floor ID and this ID could be used to identify the polygon from which the ID should be extracted to update the points featureclass. This would require some scripting.