Swiss Saver pass or Swiss half Fare Card Dilemma

We are visting Switzerland. Family of 2 Kids (5 and below) and 2 Adults.

we are going to be in Swtizerland for 8 days and our itenary is as below.
Day1 Arrive at Zurich - Take train to Lucerne
Day2 Lucerne (Mt Pilatus)
DAy3 Lucerne (Mt Titlis)
Day4 Train from Lucerne -> Interlaken (stay at Lauterbrunnen)

DAy5 Lauterbrunnen (Jungfraujoch, go via Grindelwald, First and come back via
Kliene Scheidegg)
Day6 Lauterbrunnen (Schilthorn, Wengen/Murren)
Day7 Train from Lauterbrunnen -> Zurich
Day8 Leave from Zurich

we are originially planning to get swisssaver pass First class for 8 days. (unlimited train travel) -> 1064$ for 2.

Now Iam thinking if i can manage with Swiss Half fare card ($300 for 2) and go get half price tickets on my individual travel dates.

Both these cards offer the same discount on Jungfraujoch trains and the rides for Mt.Pilatus and Mt.Titlis. so why should i spend more money on the Swisssaver pass

On top of that , iam only travelling on regular trains for only 3 days. (1,3 and 7). I don't need a pass for 8 days. I can get to pick whether i want to travel First class or not on the regular trains.

I can choose first class on the Jungfraujoch train and get half off with the half fare card anyways.

Should i buy Swisssaver First Class or Buy Swiss Half Fare card ?

iam from USA and Currency is US$.

Thanks Arno, for giving us the exact Cost on the Card.

This site says the following .
"The Swiss Half Fare Card is valid for nearly all trains, including special trains such as the Glacier Express, Bernina Express, Heidi Express and Mont Blanc Express. The same applies to bus services: the Swiss Half Fare Card is valid for about all buses, but on some special routes, a surcharge (Alpine Ticket) or a seat reservation is required.
"

So does this includes rail Europe Trains ? For some reason the rail europe seems to only Indicate Swiss Pass.

would i get half fare in golden pass train
from Lucerne to Interlaken?