I'll be in Luzern for two days. Due to limited amount of time I can only cover one of them. I'll be in Luzern end of April/beginning May during low season when many of the attractions are closed

Which should I go if I have to choose one??

Pilatus is closer, but Engelberg a bit more breathtaking imho.
You can do either the 'Golden' or 'Silver'Roundtrip to Pilatus, which is QUITE nice.
Be aware that bad weather can obscure either peak, so check the webcam before ascending on either day.

Titlis trip by rail to Engleberg is wonderful. The tri-level lift is also great, especially the fully-rotating final stage.

Titlis is amazing! We had a car so we did not take public transit to get there. I have not done Pilatus yet but will be in Lucerne end of next week and have plans to include it if weather permits.

I think you will have to decide which one to "do" as you face the weather on that very day. If you like doing a museum on a rainy day, we like the Transport Museum in Lucerne. Amazing display.

IMO the real issue with obscurity is not from below but from above. You get UP there and whamo, it's like looking down at an undercast from a plane. But the trip up can provide a great deal of compensation.

You need to plan to ascend as early as possible on a day when it is clear AT THE TOP. This can easily be found real time on the web site. The reason to go early in that clouds (and possibly rain) often roll in in the afternoon.

This happened to us on Pilatus. We went early, toured around to the various sights and then decided to have lunch which we order for outside. All this time we had bright sunshine. But just as they were to serve lunch the clouds can rolling in (very fast) along with rain. We had to run indoors and have our lunch there - and use our hooded jackets to get back to the cog railway to descent.