Milan Pinacoteca Ambrosiana or Brera Art Gallery

I've not done Brera, just Ambrosiana. I was blown away by it. It was relatively uncrowded on the late September day that I went. There were a number of what looked like university level student groups including one where the guide stood in front of the Raphael cartoon of the School of Athens for waaayyyy too long, lol. It's not that he was even pointing at things. They finally moved off and I was able to get an unobstructed view. I spent quite a bit of time in the room where they have Leonardo's Codex Atlanticus as well. I move fairly slowly thru museums in areas that interest me and quickly in the galleries that don't catch my interest. I'd say I spent 1h15m-1.5 hours in there.

I went to the Pinacoteca Ambrosiana on the suggestion of the guide from my Last Supper walking tour. Very glad I did. It took me a couple of tries to find it, but once I did it was worth it. I had the place to myself and discovered the room with the cartoon for School of Athens by accident. I spent a long time staring at it in wonder.

"t took me a couple of tries to find it,"

I can see that happening! Fortunately I was staying at Hotel Gran Duca di York which is right across the street from one of the sides of this museum so it was an easy add.

Thank you all for your comments. Decision is made! It will be the Ambrosiana.

I'm another one who went to Ambrosiana but didn't get to Brera. I went on a rainy Otober day and it was quite empty. Although I also hoped to get to the Brera, I chose Ambrosiana for location given limited time. It is just a short walk from the Duomo. It is a manageable size museum with an amazing collection. I think I especially appreciated the Da Vinci drawings and notebooks there after recently having seen the Last Supper. I too got drawn in by the Raphael School of Athens cartoon (preparatory drawing for a fresco) and explanatory video.

We did the Ambrosiana with a guided tour before continuing on to see the Last Supper. Excellent museum and a great choice.

I see everybody here went to Ambrosiana.
I think that the people more likely to be found in this area will prefer the Ambrosiana, that has a "small museum" or former private collection feel, while Brera is one of the Italian large institutional museums. This somewhat shortchanges Brera, that anywhere in the world would be considered as a primary national destination, while in Italy is in the second tier after the large museums in Florence and Rome. Personally I would start from Brera - the Hayez "Kiss" painting is to be seen in reality to believed - but I understand that most people will like Ambrosiana more.
While we are at it, I can suggest the usually overlooked Poldi Pezzoli museum, another formerly private collection.