Just had a long weekend in Engelberg (7-9 March). Good train links from Zermatt and stayed at the Angel's Lodge which was comfy, in a good location and had an outdoor hot tub. We are 2 middle aged advanced, but by no means expert skiers who are getting more and more into off-piste, though to be fair this trip was booked so late in the day we had limited choices of resorts within the 2 hour radius of Zermatt airport and basically had to plump for Engelberg as the best available. We had 2.5 days there.

The downsides: it's been said before, but the lift queues were awful first thing on Sat morning. The weather was good and there was still some fresh snow to be skied from a dump midweek. Happily, we had an instructor who could by-pass the queue at the bottom. There are no ski school only queues up the mountain, however, so we were stuck in the queues with everyone else.
On-piste skiing is relatively hard above midstation; steep narrow reds that got skied into bumps early on in the day. The run back down to the village was a nice cruise. Beginners areas are poorly linked into the main ski area. It's not a resort for those who want cruisy on-piste skiing

The plus side: off-piste. You can see why it deserves this reputation from the tracks all over the mountain.
We had a half day off-piste instruction (well, guiding really) and got to sample what Engelberg is really about, and finished our morning doing the Laub, Despite the warmth, the shady side still felt soft and fluffy and was not completely tracked out. A real highlight. Did it again on the Sunday, and thankfully the queues at the bottom were not half as bad.
The town is nice though more "towny" in architecture. It is not plagued by traffic and there are nice restaurants and bars. Be warned though, at the weekend you need to book! We had an excellent dinner at the Ski Lodge.
The views and scenery are amazing. There are some good mountain restaurants with table service. I recommend the Berghaus Jochpass in particular.
Would I go again? Yes, possibly, but it depends on the snow and the availability of guides for exploring the area properly.