What benefit would I get from using Apple Compressor instead of just exporting from Final Cut Pro X?
The export settings you are using in Final Cut Pro X are preset Compressor settings and the export itself is actually using the Compressor engine (but with no user control). Compressor allows you control over those settings and to save your own custom presets.

For instance, you may want to export an MPEG2 file with a particular bitrate, letterbox 16:9 footage in a 4:3 file, export to Vimeo with custom settings, or any other number of possibilities. If you wanted all of these outputs, you could batch process them. These, and other, codec/compression options can be configured in Compressor and saved as custom presets. Those saved custom presets then appear as available Share options in FCPX.

Compressor allows for encoding without requiring FCPX to be open, or for converting files that don't originate from a FCPX project among other benefits. It also provides a preview window that allows you to compare your source video to processed video before committing.

I still sometimes use Handbrake for h.264 files. It's very fast, clean, and free. In those cases, I will export a ProRes "master file" out of FCPX to bring into Handbrake.

Compressor is not a perfect program, but it is very useful. A lot of it depends on your workflow needs. If you like exporting directly from FCPX, but need custom share options, then Compressor is probably worth it  for you. If you are content with the presets or a workflow with other software, then perhaps not