White sox have had 50 winning seasons in 115 years as a franchise and have been a much more stable franchise. The only thing the white sox lack is postseason berths, but great runs by the yankees, A's, Royals, Indians, Twins, and Tigers have prevented the sox from reaching the top. Many years the white sox were second place they had a good record and the team that placed ahead of them ended up in the world series.
Yes. The Redsox definitely have the upper hand when being compared to the Cubs. Although I can honestly say that I'm not a fan of the Redsox, I can say that their talent pool is much deeper than that of the Cubs, and the ownership of the Redsox also has much deeper pockets. This enables them to be the better team based on talent and payroll alone.
If we look at Baseball as a game of metrics, it's obvious that the top team in Chicago are the Cubs. True, they haven't won a World Series since the Ottoman Empire existed, but when you combine those wins with their NL pennants, division titles, and wildcard berths they've got a verified 24 times of coming out near the top. The White Sox have only done that 14 times in their history.