Combined business/leisure will take us to both locations, and our itinerary will allow 2 nights in one location and 3 in another. Thoughts on which location we might benefit from the longer visit?
I'd say Prague.
Prague without a doubt; it's almost ten times the size of Salzburg in terms of population. I think 3 nights is too short a visit to cover Prague well, but it's true that some visitors are bothered by the crowding in some tourist areas, such as on the Charles Bridge.
Wikipedia lists some of the main sights and museums in Prague: https://en.wikipedia.org/wiki/ListofmuseumsinPrague
For some reason that list doesn't include the stunning, Art Nouveau Municipal House (Obecni Dum). There are tours offered of the interior. Anyone remotely interested in photography should pay the photo fee; the architectural details are beautiful.
Municipal House and the Museum of Communism were my favorite sights in Prague, but there is a lot to see there. The Portheimka Museum showing contemporary glass is very worthwhile for anyone interested in art glass.
A close call but I would go with Prague. Your three nights translate into two days, one for each side of the river. I's a long uphill walk to the castle area but well worth it.
I have been to both cities, and I definitely vote for spending 3 nights in Prague! For museums, we really enjoyed the Museum of Communism and the Alphonse Mucha Museum.
Thank you all very much.