Mostly the "utopian"-style aesthetics and technology, along with a much greater opportunity at sandboxing it up by experimenting with hybrid cultures. Also, the ability to explore how a free/liberal society operates in a world where the other nations don't care one bit for it (unlike IRL, where if you're not a democracy you're ebil). I just like the worldbuilding scope that the Fed provides.
Oh, and teh conspiracies. I've used the image before, but a group of old men in sci-fi Victorian suits, sitting in an ornate room on wooden furniture, consuming beverages and tobacco from across the cluster, discussing how to exploit the latest media frenzy taking place in the room's holofeeds to forward their goals. Not that my character supports that, but is definitely a traditionalist/idealist fighting against the opportunistic puppeteers. You can be a patriotic Gallentean without being patriotic Federation, or some such.
Thirdly, the contrasting of highly advanced civilian technology and super hi-tech cities with communities that barely have any technology in them to begin with. One of my more enjoyed elements of sci-fi.