Fiber optics can run all around your studio without generating hum, crackles or farts in your audio. With inline amplifiers they can run 500' without loss. You can't tear up the shielding wrapping them around your arm like a macho 12-year-old because they don't have shielding. They are dirt simple and you don't have to pay a huge premium for connectors that were soldered on correctly. In ADAT mode they will carry wordclock from one device to another. Not only that, but you can look at the ends to tell which direction the signal's going (if you see a red light, you're looking at one to connect to an "In"; no light, connect to an "Out" with a red light showing).
On the other hand, they are digital, so obviously you give up the analog warmth inherent in old, frayed, buzzy shielded cables with the ends held on with duct tape.