What is the benefit of using Gonoline-Euroline in combination?
Looking at your other question, I think there's some serious editing that needs to be done to clarify this question.  

Still I think there is a quick and easy answer to your question.  Gonoline media makes an excellent transfer media.  If you are out in the field some where and want to take a swab for further analysis, you could easily choose a gonoline media for transport.  Then you would want to follow that up with some selective blood agars that might show a pathogenic species that you were looking for.  Thus to use gonoline media with any other medium, is merely to preserve your sample for plating on your diagnostic media/agar later.

Again, looking at your related question, I could only guess that you meant chocolate agar, because you might be hunting Neisseriaceae (which you should put in the question if you are).