You're right: Berlin and London are both great cities, and very similar in what they have to offer. I find Berlin slightly more interesting as a city, with strong history and modern art. Best place in Germany - but still German
The city of London, is almost as interesting as a city, with plenty to see and do. Personally I prefer London, mainly for it's atmosphere or ambience. English culture easily beats German culture (which is almost an oxymoron) - and London is very multi-cultural on top of being British.
But as you say Berlin is also less expensive. Since you ask for "reasonably priced" advice and have already been to London, I would suggest Berlin.
Btw Amsterdam and Bruges are great places, too. Regardles of your choice of Berlin or London, mrs. Rum and you are in for a treat. Don't forget to try the Dutch "coffee" and Belgium beer. I can recommend the Westmalle Dubbel, but you'll be spoiled for choice in Belgium