I've done two Viking - both on the Rhine - and two Tauck - one on the Nile and one Danube. I prefered Viking for a couple of reasons: 1) Viking is dominant in Europe and has the best docking positions; and 2) more independent, primarily because of the docking positions and how easily accessible the boats are. There were more excursion options with Viking and Tauck had one tour at each location or you were out of luck (this may differ in the summer months with more options).
What are your start/end cities on the cruise? Our itinerary was Vienna to Nuremberg, then we did Budapest and Prague on our own to bookend the cruise. In Budapest, your 18 & 16 Y.O. might enjoy a Ruin Pubs tour.
I'm a very independent traveler, and *love* river cruises. For other lines, I'm looking at AMA for a Douro next fall and really liking their itineraries and the look of the ships.
Hope that you have a ball!!