The cylinder choke might perform better than the modified choke at 20 yards. Tighter chokes deform buckshot coming out of the barrel, causing a few of the shot to go off the target. I would say you will get 6 of the 9, #00 buckshot in a pizza box at 20 yards with 2 3/4" shell. There are 15, #00 pellets in a 3" Winchester Super shell. You really need to find your own pizza box and try it on your own.
You would really need to pattern the ammo you select out of the barrel you have to see how it performs. Also a cyl bore can pattern pretty well with some of the newer was designs like Federal Flite Control wads, or Hornady TiteWad.
The newer shells have shot cups and buffering to protect the shot form the choke. My 20 gauge double is choked Improved and Modified. 20 pellet #3 buck patterns 5" I and 4" M at 7 yards while my cylinder 12 gauge patterns 6" with 9 pellet 00 buck at 7 yards. With cylinder you can expect approximately 1" per yard.