Best of a weekend in Hamburg and Berlin?

Greetings!
I had 5 days in Berlin and still didn't see all I wanted- will you arrive there Sunday morning or have stayed overnight from Hamburg?
A surprising highlight was the Trabi Tour:
http://www.trabi-safari.de/index.php?language=en
I was afraid it would be kitschy but it was fabulous. (I was fortunate to have an electric one!) The guide was informative and humorous plus you drive past iconic sights in the process. It's not far from Checkpoint Charlie (that small museum was interesting, too).
You'll need an early start to the day, but could see the government buildings from the outside. And the Holocaust Memorial.
Touring the Eastside Gallery Wall was memorable, too. Since these are all almost entirely outdoors, that should help with your compressed time.
I'm sorry I can't help with Hamburg. Have a wonderful trip!

Hamburg has arguably the largest model railway in the world (Miniatur Wunderland) - we were there for most of the day.
During our weekend, as well as that, we had a harbour boat trip, went to the opera, visited a museum of illusions and had some good meals.

I would just make a list of places you want to see, group them geographically and see as many as possible. If it were me, I would probably spend the most time in Berlin, as it has so much to see and do. Hamburg is a cool city, but Berlin is really incredible.

Keep in mind that most shops will be closed on Sundays by law in both cities, although they will be open at the Hauptbahnhof and other transport hubs.

suggestions about how to make the most

Define content of most, e. g. interests or not-likes. And which weekend?

Hamburg wasn’t our favorite stop for two days but that was just us. Two hours of miniature trains was more than enough though many folks spend the entire day. A very pleasant surprise was to discover Lüneburg about 20 minutes away by train where we spent our second day. It is perhaps the most beautiful small town we have come across in many years of travel. I’d prioritize Berlin which has so much to see. Different strokes as they say. Safe travels

here's one way to do Berlin - 36 Hours Berlin

For Berlin, to get a sense of the city, you might follow the Rick Steves walk along Unter den Linden. While near the Brandenburg Gate, if you can get tickets in advance, visit the Reichstag dome. Then visit the Berlin Wall Memorial if it's of interest, and then to Alexanderplatz to see Berliners out enjoying their Sunday.

We spent 4-5 nights in Hamburg, and visited the model museum which is fun, then day trips to Bremen, Lubeck, and Lune. Hamburg itself is so-so. There is a Beatlesplatz which is just a metal sculpture in the street. There is a Brahms museum which was closed.

Berlin - I found it depressing - a lot of soviet era aging apartments with grafitti everywhere. And the place is full of young clubbers - who are at raves all night. I took off early and went to Dresden.

If I was you, I would skip Berlin, and get to the know the area around Hamburg better.

"Hamburg is a cool city but Berlin is really incredible." How utterly true !

I have been going back to Berlin every trip since 1971, missed it once in 1977, ie, 26 Berlin trips, twice during its commie days, the last time for that was in August 1989.

The city is absolutely fascinating, indeed "incredible" if you are seriously into its culture, history aside from its commie and Nazi history, obviously. Berlin was known prior to WW2 as "Spree Athens"...check out its songs, those traditional chansons.

Historical Berlin, if you're into that , is Berlin east of the Brandenburg Gate, ie from Pariser Platz eastwards.

Bottom line: if you end up with time only for one city, then I heartily recommend Berlin...fantastic choice. I like Hamburg too, the cultural center of North Germany.