Hi Sagarsiddha -
I was traveling and di not have time for an answer.
Arno gave the accurate and and succinct version.
To amplify slightly.....Zürich is a city that rewards spending significant and leisurely time, exploring museums, music, and cultural things. I probably like Zürich better than any other Swiss city, but it is not because of things that you can easily see in a one day quick trip.
Luzern has a very scenic location, with high mountains surrounding it, a beautiful lake with much more rewarding scenery then the lake of Zürich, and a much more scenic old town.
More tourists, too, but that is because it is attractive for tourists.
That is why I say " skip Zürich" to most first time tourists to Switzerland, unless they want to explore some really good art museums, go to the Tonhalle for a concert or take a walk from Uetliberg to Felsenegg with a stop at UtoStaffel for lunch. ( 3- 5 hours required for walk plus lunch.)
(By the way, near the station in Luzern is a major collection of Picassos and Klees in the Rosengart Collection, if that interests you.)