Hello Noagoukoam79
Does Saver Day Pass provide me the same thing for cheaper prices?
Not entirely. The Swiss Travel Pass gives you certain discounts for mountain excursions, the Saver Day Pass does not. The Saver Day Pass cost is raising the nearer the travel date, or can even sell out. The Swiss Travel Pass cost is the same, no matter the time of purchase.
It all depends on what you plan. First finish your planning, then think about the ticket, not vice versa.
With only three days, you have to plan your trips well. And if you are there for the first time, then you should Lucerne not give a miss but Zurich. Also, you should choose a good base that is well situated to minimize travel time. Lucerne or Bern could serve as such.
Use www.sbb.ch/en to look up itineraries and to get an overview of the travel times required.
Kind regards,
Roland