Jay, our family just returned from Switzerland, with 2 nights in Engelberg followed by 3 in Lucerne. We had been to Paris before Engelberg, and really liked the calm and serenity in Engelberg after our busy days there. We asked our hotel if we could have a late checkout to be able to stay a bit longer, and if we could have, we would have shifted our Lucerne nights to stay in Engelberg another night or two - so that is a different perspective to offer.
We arrived on Friday night, learned of promising weather on Saturday, so planned to go up to Mt. Titlis on Saturday. That was a wonderful trip for us - we spent several hours in the snow zone up there. On the way down we got off the cable car in Trubsee and explored there for a while, rowing a boat on the lake, and being surrounded by cows with their cowbells ringing as they made their way to another pasture. The day was truly memorable. The next day when we were supposed to leave, we arranged to stay later, and chose one hike from a huge list of choices, going to see a waterfall and climbing on the rocks around it with our kids. A soak in the inn's outdoor pool, then hot tub, gazing at the mountains, made for a great afternoon - and then we left for Lucerne. If we could have stayed another night, we would have all been really happy - if only to go on a different hike and explore some more. The pace there was so different from both Paris and Lucerne. A good rest for our busy traveling family.
I guess we were ready for more low key activities because we spent our time in Luzern strolling around the city, and on our last day, we took a paddlewheel steamer to Weggis for more exploring and a very nice lunch.
So, now that we are all home, my whole family is saying that they loved Engelberg, and would like to go back some day! :-)
Also, because we went to Mt. Titlis, we did not feel any need to do a day trip from Lucerne to Mt. Rigi or Mt. Pilatus - but it looks like those are good trips, too - without snow. We wanted snow. We got it - and also had the fun of seeing others experience snow for the first time, which was amusing to my Midwest family.