Vienna in November - Itenerary

Budapest
- more spread out (need to use the metro to get from place to place)
- castle exterior is lovely, but no interior tour
-they'd probably love the Fisherman's Bastion, though, if they like castles
-a lot of the history/sights might not be appreciated by 4-6 year olds (Museum of Terror, Great Synagogue, Hero's Square, Opera)
-there are the baths, which would be fun and give a nice respite to touring
-has a big ferris wheel (not sure if it's seasonal)
-less expensive
-uses a different currency than Vienna

Salzburg
-more compact
-castle looks more like a storybook castle
-can tour the inside of the castle
-cool signs on the shops in town from before people were literate--even a 4-year-old can appreciate these
-can show them the Sound of Music before the trip and look for the applicable sights in Salzburg (e.g. the horse fountain and the do-re-mi steps)
-more expensive
-uses the same currency as Vienna

I'm sure there's lots I'm forgetting, but I guess I'd lean toward Salzburg with kids that age. That said, I loved Budapest and spent 6 days there, whereas I spent only a day in Salzburg. But that's me, as an old fart. :)

My only trip to Salzburg was after Thanksgiving and I was so cold I went from one café to the next to warm up. It sounds like you’re leaning towards Budapest since you’ve been to Salzburg so go to Budapest. Your kids will be fine as long they are with mom and dad. You may want to sleep in Buda since Pest is livelier. I actually prefer the Buda side over Pest.
While in Vienna consider a day trip to Bratislava that’s a direct train ride away (1h). If you do go to Bratislava, take a taxi from the train station to the old town. I would also purchase Rick Steves Vienna and Budapest’s guidebooks.

I did xmas markets in 2019, and I don't think the cold is a problem if you dress right, have rain gear, and stop frequently for yummy hot chocolate. We brought a bag of hand warmers, which were great! Stay in the center of the old towns, so you can easily get back to the hotel/residence in the event of rain or for breaks. The kids should love the ice skating rinks. I would choose Salzburg as the second city.
Have a wonderful family vacation!

As a mom, I would vote for Salzburg as it is much more manageable with smaller children. The fortress there is magical, as you know. Be prepared to be cold.

I love both cities, but here’s another vote for Salzburg with small kiddos. Both cities are going to be cold, but quite manageable with the right clothes. I would try to stay in the pedestrian old city where they can have a bit more freedom and you don’t have to worry about cars.

I love the Weisse Taube, about a block from the Dom and even closer to the ice rink. They can push a kid size plastic penguin and learn to ice skate. Thanksgiving week the Christmas market should be opening, and it’s magical. I like staying close in because you can get out of the cold.