Dresden or Salzburg?

It depends on your interests:

Museums + WW2 + architecture = Dresden
Old world vibe + food + traditions = Salzburg

For museums and WWII history,Dresden is hard to beat,I have been there twice and love the city and the surrounding areas.Salzburg is very compact and definitely worth seeing,tough choice,if going to Dresden it links well with Prague just as Salzburg fits in with Munich.
Mike

I endorse mike’s reply. Do you care more about Mozart (or Julie Andrews), or about Lucas Cranach? In fairness, Dresden also has porcelain and Saxon Switzerland, which you don’t have time for. And going back to WW II, I found it charming to learn that the American Military Governor of Salzburg loved the place so much that he and his wife are buried there. Many buildings in Salzburg have a Wiederaufbauen .... plaque on the corner.

I would choose Dresden unless you are a HUGE "Sound of Music" fan or dislike spending time in museums. Dresden has the rebuilt Frauenkirche and incredible museums at The Green Vault and the Zwinger. I enjoyed my day in Salzburg but do not expect to return. On the other hand, I would enjoy revisiting Dresden.

I liked Salzburg more than expected and Dresden less than expected. But, I am not a "museum person" (nor am I a big "Sound of Music" fan actually). I found Salzburg charming and picturesque. Dresden was sort of of more interesting, but I had trouble warming to the place for some reason.

Both interesting options. Dresden is a clear culure highlight. Nothing against close Saxon Switzerland but if you look for Alpine panoramas Salzburg is clear in front.

Thanks for all of the good input! Our trip will be 3 weeks long--a Rhine river cruise, a few days in Vienna/Bratislava, a few days in Munich and a few days in Berlin. We are hoping for a good mix of museums, history, architecture, music, as well as enjoying the German and Austrian "feel". I particularly love art museums, but will try to limit it to 2-3, and know there will be plenty to choose from. We will also be doing some hiking and enjoying scenery. Hence the dilemma with these two days, since we hope to enjoy many facets of Germany and Austria.

A rather tough decision to make. Which do you prefer, Saxony or Upper Austria.?

I'll vote for Dresden because of the palaces and the Frauenkirche unless you are a desperate Mozart fan wanting to see both of Mozart's houses in Salzburg.

If you're interested in Saxony's military history, I mean prior to WW2, that's displayed in the museum in Dresden-Neustadt, the former site of War Academy am Olbrichtsplatz. Dresden was the HQ for a military district.

I particularly love art museums

Plan a lot of time for Berlin and Potsdam. A lot of less known art museums and private collections, e.g. in US nearly unknown Museum Barberini. SAP founder Hasso Plattner is providing more art from his private colection to "his" museum in Potsdam. Also other remarkable collections and currently two more big ones announced.

Some high-end street art is coming and going so quickly that even locals do not have the chance to see all of them, e.g. Mona Lisa at East Side Gallery is already painted over.

a few days in Vienna/Bratislava, a few days in Munich and a few days
in Berlin.

In this case I would recommend Dresden, simply because Vienna, Bratislava, Salzburg and Munich belong more or less to the same cultural area.
PS: it's possible to do the city as a day trip from Berlin, but a) this wouldn't do the city justice, b) there are better day trips from Berlin, and c) Dresden deserves more time, especially since the city is a great base for day trips.

Your interests should decide. Salzburg is beautiful, Old World, alpine surroundings. Last time I saw Dresden was in 1965, 20 years after WWII and terrible bombing. Ruins and empty spaces everywhere. I am sure it is different now. But it was all rebuilt. It is not really an old city.

Salzburg was bombed too (e.g. Mozart's house), a fact Austria Tourism is eager to conceal. Admittedly, damages were much lower.