Actually the quality is the same, but the workflow is different. Sending directly to Compressor, Final Cut makes a reference clip of your sequence that it uses to encode. Exporting a clip from Final Cut using the Export Quicktime creates a self contained clip on your hard drive. We find this workflow, creating a self contained movie, is more reliable. Final Cut and Quicktime in general are notorious for losing references to media in a reference clip causing all sorts of problems.
The tried and true method for encoding from the timeline in FCP is to do the Export Quicktime Movie and make a self contained movie of your edit.
One exception I might make is if you have a very long timeline with only a few clips. But if your timeline is loaded with tracks, stills and clips, and multiple audio tracks, do the Export Quicktime movie and you will be headache free.
Tilt Media Inc.
Video Production and Post