txcshooter wrote:After studying the pic there, do you mean it would be
 "easier" to hit with an Improved Cylinder...? or am I reading it wrong?  

 
On a skeet field - your best shot with the 12 ga is with a slight constriction (skeet or skeet 2).  Cylinder is more open but still fine.  The improved cylinder (sometimes called a skeet 2) is more constricted than the skeet choke but you should see no big difference.  Progressively tighter chokes tend to make it not necessarily harder to break clays - but you better be a dang fine shot and have the leads just right.  Gets real interesting on station 3, 4, 5 and 8.  Some shooters start going to slightly more constricted chokes as they go down in gauge (20ga, 28ga) or bore (.410).
On the trap field - tighter chokes (light mod, mod, improved mod) are norms - especially when you start handicap rounds.  But - that is different game.
Five stand and sporting clays - have lots of different chokes handy and a speed wrench...