Music or Ballet - Munich or Berlin?

They are both first class. I don't think anybody but a true virtuoso would be able to discern any difference.
The important thing is that most of these shut down in the summer.

Edit - I see that the Bavarian State Opera continues to the end of July with the Munich Opera festival.
https://www.staatsoper.de/en/index.html

Berlin has 2 opera/ballet companies. Deutsche Oper Berlin, and the State Opera Berlin.
State Opera-Berlin runs through the end of June, then a run of West Side Story in July.
https://www.staatsoper-berlin.de/en/

Deutsche Oper Berlin runs pretty much through the end of June and restarts August 22
https://www.deutscheoperberlin.de/en_EN/calendar

As in the USA, summer is not the best time to find large indoor musical events. In addition, major cities have devoted followings and it can be very difficult to get tickets, unless you buy months in advance. (At least that's relatively easy on the Internet, but you have to make sure you have found the legitimate source of real, first-issue tickets.)

Although there has been debate about how many opera companies one city can support, Berlin still has multiple opera companies. Some viewers don't care for the modernistic Philharmonie building in Berlin. But I think Berlin has a slight edge over Munich. (I haven't visited BOTH of those cities on one trip to Germany, because it's such a culturally rich country.) We once settled for a chamber concert in the smaller Berlin Phil room (which is plenty big) on our arrival day, because that's the only way we could get a concert that week! It was a struggle to stay awake, of course!

Another option you can consider is seeking out summer festivals. It's not near either city, but because WE missed it, I noticed that distant cities like Schwerin can have major arts festivals at the height of summer. When I've wanted to see a particular venue, like the Marmoreean Saale (sp.!) in Salzburg or Smetana Concert Hall in Prague, I've been happy to settle for short "tourist concerts."

Clearly Berlin - you will have much more choices (houses, stages) in Berlin - three opera houses alone. And not only quantity: the Berlin Philharmonic Orchestra is very often considered as one of top 5 symphony orchestras worldwide. Staatsballett Berlin is also performing remarkably.

In summer months we have a lot of open-air or special weeks around classical music.

Between the two cities, absolutely Berlin...three different symphony orchestras in Berlin....bumped into a summer open air concert (Konzert im Freien) on a Sunday ca noon a few years back in the Gendarmen area, totally by accident, just followed the sound of the music.

It was the Berliner Sinfonie conducted by S Rattle (sp ?).

As expected they played Beethoven...utter fantastic, captivating, mesmerizing, as I joined everyone else standing there and listening. Rattle addressed the audience afterwards in German too, absolutely one the highlights of that trip.

Three symphony orchesters? :-)

Well - a few more orchestras in Berlin. Even if you count only the big professonal ones you can listen to seven different ones. Plus choirs.

Berlin is a city full of musicians. Sony Music will relocate its European HQs to Berlin to be closer to their artists.

If you enjoy the ballet, go to the ballet. If you don't, go the concert.

Good , thanks for the information...stand corrected.

I think Fred may have intended to refer to the multi-year controversy over whether the city of Berlin can afford to continue to have THREE OPERA houses in operation. One problem is that the Komishche Oper was behind the Wall, and it would be an insult to the ... er ... new citizens to pick their opera house to close down. As an American, it's startling to hear about a ... Social Democracy ... that is coming to believe that there are limits to what the state can do for its people! Although presumably, interest in opera is suffering gradual cultural decline there too, if at a lower slope rate.

I think Fred may have intended to refer to the multi-year controversy
over whether the city of Berlin can afford to continue to have THREE
OPERA houses in operation. One problem is that the Komishche Oper was
behind the Wall, and it would be an insult to the ... er ... new
citizens to pick their opera house to close down. As an American, it's
startling to hear about a ... Social Democracy ... that is coming to
believe that there are limits to what the state can do for its people!
Although presumably, interest in opera is suffering gradual cultural
decline there too, if at a lower slope rate.

I guess that Fred can speak on his own - what he already did few times here and I fully appreciate to read his contributions.

My view on your points:

• Facts: be informed that Berlin has 3 opera houses (Staatsoper, Deutsche Oper and Komische Oper) plus 2 large classical music concert houses (Philharmonie and Konzerthaus) plus other locations like Großer and Kleiner Sendesaal in the Haus des Rundfunks plus special event locations like the concert hall of UdK (Berlin University of Arts).
• 2 of the 3 opera houses were "behind the curtain": Staatsoper and Komische Oper. By the way: culturally there are two valid views from "behind the wall" - and one is not better than the other. There is no winner. I am happy that a stupid "3 are too much"-thinking was not followed because especially in culture topics it is valid that 1 + 1 > 2. In Mathematics 1 + 1 = 2 can also not be proven, it is an axiom, like faith - believe it or not :-)
• The mentioned controversy is over since around a decade: all three houses are fully budgeted and had huge investments in renovating buildings and interiors - we would not do that if we would not stand behind it for the next decades.
• "Social Democracy" is politics and over 150 years old in Germany - you likely mean social market economy which the western part of Germany has since the 50s. I honestly suggest to read Karl Marx once a lifetime, e.g. "Das Kapital" - the earlier the better.
• Every economic system has its limitations what it can afford but some nations care, others not. All EU countries agreed to have a debt-equity ratio (compared to gross domestic product) of max. 60%. Germany is back in that limit since last year. USA have a ratio of over 106% which is from a perspective of most Germans really not understandable - you cannot spend more than you earn but I guess that approach of wasting future generations' welfare is on of the biggest cultural differences between USA and Germany, similar to understanding of quality. And I think that especially the USA politics are a horrible example for "there are limits to what the state can do for its people", just think of nearly annual shutdowns which we neither have in Germany nor in most of other European countries. Tons of other numbers and indicators on top let Germans shake their heads about what we perceive.
• The assumption of suffering or declining interest in opera and classcal music is fully wrong: Germans spend a lot of time and money for classic culture - spendings are raising year on year. One of the most expensive examples is the new built Elbpilharmonie in Hamburg. Sold out classic open-air events with up to 20,000 visitors (in Berlin) are just another indicator for that - even if they lost their old picnic spirit. Furthermore Germany welcomes millions of visitors every year who also want to take part in our outstanding manifold and quality of cultures, culture and events, e.g. Bayreuth Festival.

Admittedly I thought that Berlin had 3 symphony orchestras which is incorrect and inaccurate, was not referring to the opera houses.

I agree with MarkK that Berlin has the edge. Apart from Berliner Philharmoniker (one of the best symphony orchestras in the world) I would also like to mention Akademie für Alte Musik for baroque music.