MotionBuilder provides the following methods of saving objects, assets, and takes as .fbx files:
FBX files exported via Python Tools > FBX Export > FBX 2010 tool or the FBX Converter tool are FBX SDK files and not MotionBuilder files. This means that anything specific to MotionBuilder will be discarded (story information, Devices, ect). Also, FBX file format version 2010 does not support the MotionBuilder 2011 Animation layers.
Regardless of the saving method you choose, you have further save options that let you select the assets, settings, and takes to save. You can also specify Saving options such as embedding media and saving a separate file per take.