Beijing sits in a geographic bowl (trapping pollution) and is inland from the coast compared to Shanghai. It also gets hit with dust storms from the desert to its west, all of which lead to it being "crazy bad"[0] in relation to Shanghai.

re: "crazy bad" being tweeted by the US Embassy in Beijing -- a cautionary tale on string sanitization. "The "crazy bad" terminology – which was at odds with the normally sober and scientific language of the Twitter account – appeared to have been a joke embedded in the embassy's monitoring program and triggered by a reading that was off the normal scale."

[0] http://www.theguardian.com/environment/blog/2010/nov/19/craz...

According to the data from this page: http://kopf.github.io/chineseair/ Beijing seems to typically have higher pollution levels than Shanghai.

Beijing is generally worse more often, partly because they get hit by dust carried from the increasingly large Gobi Desert in addition to all the man-made pollution.