ability to play  

I am not a big baseball fan but I would say that it has to do with multiple factors. Maybe the White Sox are better with money so they can go out and get better players, plus maybe they have a better coaching staff. It could be that the players mess better as a team than the Cubs and it couls also be because of who they are playing, maybe the Cubs just play better teams than the White Sox.

I think there is so much more that goes into building a good team than just getting good players. You could have a whole roster of mediocre players and still win lots of games if the coaches are good, the team plays well together and if the players have heart.

Because they're an entirely different team. That would be like saying why do the Steelers win Super Bowls and the Pirates can't even get to a playoff game? Just because they're from the same area means nothing, other than perhaps a fan base.

Cubs tend to put out less money for their players in general, have a totally different staff to train them and a whole different style of players even.

It's the make up of your team and how they are coached.
Example. White Sox play small ball. Get a guy on. Move him over to second and try to bring him in from there. They don't just really on the homerun.They try to put pressure on the other team. The Cubs don't like to play small ball. They really on 3 or 4 players to drive in runs. The Sox entire lineup can drive in runs. The pitchers the Sox had were dependable and reliable, the Cubs staff is imconsistant at best. The philosphy of the managers is totally different.