Swiss Travel pass

Jan - While you are staying in Zermatt for those 4 nights, are you planning to take the train and do day trips to visit nearby cities or towns via train? The same applies for your stay in Chamonix.

Here is a map of the Swiss Travel Pass and Half Fare Card validity:

https://cdn-doc.myswissalps.com/docs/default-source/rail-network-maps/swisstravelsystem.pdf?sfvrsn=7788603a_36

Note that the Swiss Pass with take you to Zermatt but will only cover 50% of the lifts and trains from town into the mountain areas (Gornergrat, Sunegga, etc.)

The Swiss Pass will also fully cover the journey from Switzerland to Chamonix, but not any of the lifts around Chamonix. The Half Fare Card will not reduce that fare beyond the Swiss/France border at Vallorcine.

Yes, we plan to take the trains to nearby towns especially if the weather is not good for hiking. But we would like to do some hiking in those other towns too. I am having a hard time deciding if it is more economical to get a Swiss Travel Pass or just buy a regional pass in Zermatt and also in Chamonix.

I don't think that a Swiss travel pass will work out as you only have 2 long-distance Swiss journeys. In Zermatt it would only give you 50% discounts on lifts, the fares for e.g. Gornergrat wouldn't be included.
I would even say that I'm almost sure it's a bad deal. You'd need at least a 4-day Flex pass (since you stay 5 or 6 days in Switzerland), that's 323 francs. To which you need to add half-price mountain ride tickets.

However, a 120 franc Half Fare Card would do exactly what it says on the box: 50% off all train rides and most pedestrian mountain lifts including around Zermatt. Add a little over 100 francs for reduced-price train travel to/from Zermatt, and the total is approx 225 francs instead of 323 with the Swiss Pass. Still excluding mountain rides.
The fare from the Swiss border to Chamonix is negligible, a few euros.

Not sure if you followed the math, but you can do the math yourself.

You could get the Swiss Travel Pass Flex and travel by train at the dates you choose to.

If you think you will have the energy to be able to see more than one town in a day than the 4 day Swiss Travel Pass may work especially since the sun does not set until 9 pm that time of year allowing you a longer day to see things far and wide but if not I agree the Half Fare Card is the way to go.

Thank you to everyone for your much appreciated assistance.