Shanghai has better tailors.

From a foreigners perspective, Beijing is the political capital of China.  Cultural history is also

very prominent in Beijing. Shanghai on the other hand is  very cosmopolitan more like New York.

I like Beijing more.

I really like to visit Beijing and Shanghai one day!

For me Beijing and Shanghai are completely different cities!.  I really hate to travel to big cities or metropolis (both of them are big cities). But when I arrived to Beijing, I was fascinated. i really like the combination that Beijing has between the past and the present, although it's a very large cities, it still maintain old the historical places and buildings designed during the chinese empire, and when you walk through the streets you really can fell that cultural vibration. In Beijing I really could fell the real chinese culture that started to grow up since the beginning of the republic.  

In the other hand, Shanghai it's a huge city, with lots of buildings, you can notice that you're in a city that comes from the developing of worldwide commerce, but no culture. Shanghai really is a world city, you really can understand what globalization means and the new chinese economic power.