A frequent retort to criticism of the White Sox farm system, particularly from Kenny Williams, is that the results speak for themselves. Helpfully, Baseball America gives us at least one qualitative data point on those results, as they annually rank farm systems not only on their current state but on what the farms systems have actually produced.
In their estimation, since 2009, Baseball America ranks the White Sox #19. Based on their own prior rankings, this appears to lend some support to the White Sox' assertion about their farm.
In those years, Baseball America ranked the White Sox as follows:
In the blurb accompanying the ranking, Jim Callis wrote:
19. WHITE SOX. Chicago stole Chris Sale with the 13th pick in the 2010 draft and is starting to see its $10 million investment in Dayan Viciedo pay off. Addison Reed, Jose Quintana, Nate Jones and Hector Santiago bolstered the White Sox pitching staff last year, though they’d like to reverse their trade of Hudson for Edwin Jackson.
One related point that the White Sox tend to make is that they promote players faster than other clubs so the likes of, say, Chris Sale or Addison Reed, aren't in the White Sox rankings in a given year when, on another club, they may have been.