To the best of my knowledge, this matter has never been debated (in its own thread) on FT. As such, here goes (IMO):

-for tourists that need to pick one over the other, Beijing wins by a country mile
-During Shanghai's construction boom, Beijing was better, and during Beijing's construction boom, Shanghai was better
-Beijing people are nicer (and inherently cooler), but Shanghai people (including the expats) tend to be smarter --> interesting conversations
-Shanghai has better food
-the shear scale of Shanghai can be overwhelming at times --> we need our spa time
-it is easier to fetch taxis in Shanghai
-I loathed Shanghai during the aftermath of the "Tom Cruise" era, which made the city "trendy", but most of those obnoxious people are back in New York and Taipei now
-Shanghai smells worse
-Beijing has better water
-From Shanghai, I can fly to HK and back for $200... compared with $600 in the case of Beijing

Having gotten all that off of my chest, I am inclined to proclaim that Shanghai wins by a hair. But, there really isn't any need to compare; we can enjoy both cities, thanks to the new train. In fact, I'm in the process of crafting my next 12 month plan and am thinking about a 50-50 split.