Swiss Travel Pass or Swiss Half Fare?

You’ve posted this thread twice. Would be good to delete this one and just have one going.

Since your first posting was incomplete, I think that's the one you'll want to delete.

The Berner Oberland Regional-Pass will give you more complete coverage in the area where you'll be visiting. Here's the web site link:
https://www.regionalpass-berneroberland.ch/en/pass-and-infos/area-of-validity/

You actually will be going below Wengen to get to Grindelwald (it's in the next valley) and to get to Mürren and Gimmelwald (they're on a different cliff on the other side of the Lauterbrunnen Valley, so you have to take the train down from Wengen to cross the valley to the other side). Here's a panorama map to give you a picture of the layout of the area:
https://www.regionalpass-berneroberland.ch/assets/karte-und-partner/Regionalpass-Panoramakarte-2017.pdf

Thank you so much! I’ll check into this!

The Travel Pass is more convenient but the Half Fare Card usually save the most money, provided you have more than 240 CHF worth of full fare tickets to buy.

During how many total days are you traveling within Switzerland? It makes a difference whether you're comparing to the price of a Swiss Travel Pass for 3 or 4 consecutive days, at about $245 or $290 respectively, per adult, or whether you'd have to bump up to a more expensive one.

We will be there 4 full days then heading to Italy

That sounds like travel on 5 different calendar days, in which case you'd have to pay for either a separate ticket, or a more expensive Swiss Travel Pass, or both (a pass for 4 days spread out costs $335). Your cheapest day might be one in the middle. Or the Berner Oberland pass offers a 6-day version for 310 CHF but does not cover Zurich-Lucerne (25) and Brig-Domodossola (15).

Thanks all! I appreciate all your advice:)