Due to a mistake in our airline reservation we have an extra day to spend in either Budapest, Prague or Vienna. We are flying home from Prague and so the easiest thing seems to be to add 1 more night making it 5 nights in Prague. (We are presently staying 4 nights in Prague.) We are staying 3 nights in Budapest then 3 nights in Vienna. Should we try to switch all of our reservations and add an extra night to Vienna or Budapest instead?
Would appreciate some advice. Thanks.

Personally, I would allocate the extra night to Budapest or Vienna -- but that reflects my tastes. Others will have different opinions. You won't get a conclusive answer here.

I gather that adding the extra night in Prague is the most convenient thing to do. I suggest that you take the easy option, and then you can tell us afterwards what you think might have been the best choice *for you*.

An extra night in Prague would be my choice. There is lots to do there or you can use the extra day for a day trip such as Terizin, Cesky Krumlov etc.

Vienna is one my favorite places in Europe, so it gets my vote. There is more than enough to keep you busy in Vienna for 4 nights. There is also no shortage of day trip options from Vienna as well (Graz or Melk for example). Although I'd just stay in Vienna for the whole time.
For the past eight years in a row, I've spent about two weeks in Vienna every March and still have things on my list that I haven't seen. Not to mention a whole list of places that I like to go back to for repeat visits.

I would add an extra day to Vienna - we did 4 Prague and 5 Vienna and I thought that worked well.

My preference - based on my interests - would be to add the day to Vienna. But what are your interests? What do you hope to see and experience on this trip?

another vote for Vienna!