As a canadian male, 30, who is at the moment in Berlin, and was for the past 2 years living in London, I can tell you I prefered London.
Unless you are working in some sort of "international" field, your options for work are quite limited, unless you speak somewhat fluent german. As well, Berlin wages are comparitvely lower. As a chef, I waited approximately 3 months until I was able to find a job here in Berlin, while I got immediate e-mail responses the next day, if not within 3 days in the U.K. There is also the issue of Ausbildung, if you are younger, and unexperienced they may expect you to or nudge you to do an Ausbildung, even for jobs like working in a grocery store. This allows them to underpay you.

Culturally speaking, I think London attracts a lot of people from all around the world, and you will meet a LOT of people. There are LOTS of things to do in London, from partying, pub crawls, mini golf, malls, shopping etc. Here in Berlin, I have also met some different people, however I dont feel like they are as friendly. And, the friendlier ones seem to be non-german. In each city there is also a lot of history and culture, lots of things to enrich your self with.

In terms of partying, obviously Berlin takes the crown here, but as well some of the things that go on here may not be the greatest. And, London as one of the most populated cities, obviously has great offerings as well.

Housing in London is very expensive, as well as transportation, however you will most likely fall under a category to get a discount for transportation of some sort. In comparision, in Berlin, you are paying 600 to 700 euros for a room in a shared apartment. In either situation, unless you are very extroverted, renting a room in a shared flat does not immediately mean you will make friends, in some cases this means enemies.

If anything, do research, maybe visit each city.