I think the Smooth bore idea came before APFSDS, since HEAT rounds don't like spinning at all.
Actualy smoothbore is used because you can achieve high velocity and with less wear on the barrel. Rifling causes friction.
A lot of resistance and friction and corrosponding increases in pressure are necessary to spin a very high velocity projectile with rifling.
A smoothbore allows maximum velocity with minimum resistance, meaning kinetic energy penetration can be maximized.
It also is unpractical to purely spin stabilize a projectile as long and thin as some of the kinetic penetrators. The required revolutions is insane.
So it just makes better sense to go to fin stabilization.
It is funny that the progression went from smoothbore, to rifling, then back to smoothbore with special rounds.
While not the intended purpose a side benefit of the smoothbore design is the gun can be used as a massive shotgun firing shot in decent patterns. It destroys infantry just like grapeshot once did.
Here is a slow motion video of it in action:
http://www.youtube.com/watch?v=Cgn1nhUEgo8
Firing
1150 10 mm tungsten shot projectiles at about 4600 feet per second.
They can also use flechette rounds which pattern even further, and penetrate like crazy zipping through civilian structures.
The most common user of the flechette rounds is probably Israel, who uses them on Palestinians frequently and has therefore generated a lot evidence on thier performance.
There is also rifles now that operate similar to the M1 gun using similar projectile designs:
http://world.guns.ru/sniper/sn46-e.htm