My headline really explains my entire point, the Sox are going to need some seasons to get up to the level the Cubs play at. Also, the Cubs all-star batters are relatively young. Unless the White Sox can make the deal of the decade, I don't see it happening. Stranger things have happened but, it's very unlikely.
This might be biased, due to me being a Cubs fan, but I tried to keep it unbiased. This is the very first year that the Sox are rebuilding, so I do not see them playing better then the Cubs. I'd say give it some time, but not one year, for the Sox to get to a level to where they are equal to the Cubs. The Cubs are the Word Series winners, so the Sox will need more than one season to get to even the equal level.