Scattergun also lets Scouts survive against Pyros much, much more easily and makes them relatively safe to engage.
Also, the -20% damage is offset by the 20% more bullets, so FAN does about the same damage as Scattergun from any range. The FAN has the same amount of spread as the Scattergun and only does 96% less damage. The thing is, you shouldn't be able to kill enemies from 15 yards away with either gun anyway.
If I remember correctly, there was a chart put up on the Steam forums which showed how if both guns were fired constantly, they would do about the same amount of damage over time.
The Scattergun's main power over the FAN is its versatility in when it can be fired. FAN, you fire two shots, you must reload, and you can't fire while reloading, even if you have a bullet left. On the other hand, Scattergun's reload animation can be interrupted at any time with a shot. That's a big deal in tournament play, which is why they don't use the FAN there.
I think that's mainly why the FAN is best for hit-and-run and Scattergun for variable situations. If you're ambushed while reloading with the FAN, you're only choice, really, is to run while unloading your pistol. If you're ambushed while reloading with the Scattergun, you probably still have about 2-3 shots left to deal with him.