Day trip to Budapest or Salzburg?

It's purely a matter of opinion. While neither city can be "done" in a daytrip, there is much more to see in Budapest, and it is a plenty "romantic" city to look at. Salzburg is more subtle, and takes more time to get a feel for. I mean, for example, strolling through a cemetery and seeing that the US military governor of Salzburg loved it so much that he and his wife are buried there.

Disclosure: I'm not big on Christmas Markets, but that's partly because US Christmas markets sell so much imported merchandise. I have also been to plenty of (non-seasonal) flea markets (like in Antwerp, for example) in Europe where imported (especially Polish clothing, I thought) makes up much of the merchandise.

In December, a key fact for me would be which city has the most available versions of Glühwein?

Have you checked on southern Czech republic and Bratislava (haven't been there myself). For a 2:20 train ride, I'd consider hiring a car service if necessary for a day in Cesky Krumlov or the 3 T's (if they have Christmas markets, I guess, for you.) The question is whether you will ever get to Budapest, otherwise.

Go to Budapest. Everything will seem like half price compared to Austria. Budapest is a world class city, while Salzburg is a comparative backwater. Ask yourself, "What would Mozart do?"

Corona restrictions are tightening up at the moment in Austria and crossing a border might take extra time.

I'd stay within Austria on a day trip for sure. Salzburg is definitely magical, so not an option to regret at all.

Budapest! Salzburg lovely but sleepy, outside of opera festival, and very expensive. Budapest fascinating, full of variety.

As of today, the Austrian border is open without restrictions.

The Budapest markets only sell local crafts and Hungarian produced products; each vetted by a review board in advance.

The Budapest markets almost always rank among the top in reviews of all markets; every review is different but Budapest almost always hits the top 5 or so.

These are all subjective as h...., and there may be some ulterior motives behind the rankings, but it gives you a general idea of the better ones to visit.

This one its 2, no mention of Salzburg: https://www.europeanbestdestinations.com/christmas-markets/
This one its 4 (and Salzburg is 2): https://www.thetimes.co.uk/travel/destinations/europe/best-christmas-markets-holidays
This one Budapest 3, Salzburg 6: https://www.roadaffair.com/best-christmas-markets-in-europe/

I wouldn't call Salzburg backwater: its a pretty city and either would be a good choice.

I find both places to be great (though I find most places/things to be great). Having been to both Christmas markets, I think either will more than satisfy your hunger for such a market. If I were in your shoes and already had tickets to Budapest, that's where I would go. If the borders tighten, you can always go with Plan B.

The time for cold feet are over. Budapest it is! wtm1 gave me excellent ideas and guidance. I will report back on my great time.

Again, a sincere thank you to all who have helped me by giving their opinion and ideas.