Players move through the Sox system based on how well they swing the bat, as opposed to the Twins, who will not move a player up a level if his defense is suspect. The Sox need to change this philosphy, and start to require players be able to play their position. The Twins are also very conservative on how they promote pitchers, and will usually not promote a pitcher until he spends a full season at one level, as opposed to the Sox who have a tendency to rush pitchers, particularly starters.
The Twins also spend more money on scouting, and employ more scouts than the Sox, because their philosphy is to build their team from within as opposed to paying free agents, while Kenny uses his minor league talent to acquire major league talent. You can make the argument for or against this philosophy and make a decent argument, it is more a matter of opinion, I feel you get a better team player out of a player you developed in your system.
In the end it comes down to money, with the signing bonuses a lot of teams are paying to top draft picks, they want a as fast a turnaround on that investment as possible, even at the expense of bringing up a player that is not ready to play at the major league level. Brian Anderson is a prime example of this.