Swiss Flex Pass- 4 day or 8 day?

The Swiss Half Fare Card is valid for an entire month.

You have 2 options worth considering:
1/ Buying a half-Fare Card as stated above (120 CHF), then purchase half-price tickets for approx :
- Swiss border -> Zermatt = 40
- Zermatt -> St Moritz = 90
- St Moritz -> Luzern = 50
- Luzern -> Zürich = 15
So about 300 for the whole thing

2/ Buying Saver Day Passes for the Swiss Border-Zermatt, Zermatt-St Moritz and St Moritz-Luzern days, 60 days in advance if possible, and a full-fare ticket for Luzern-Zurich.

If you find the cheapest Saver Day passes (52 CHF), the savings are massive, since total cost is only 175 CHF. But if you plan excursions from St Moritz or Luzern, then you might find that the half-fare Card is a better deal.

balso's analysis shows that when it comes to saving money, the Half Fare Card almost always beats the Swiss Travel Pass. You're paying a premium for convenience. The 4-day flex is 323 CHF, but you'll pay about 300 CHF for your 4 travel days with the Half Fare Card, plus you will have it for discounts on any other excursions you might want to take.

Another point, the 3-day flex is 267 CHF, a 56 CHF savings over the 4-day, and the only reason for use is to cover a 30 CHF full fare ticket from Luzern to Zurich, so a 3-day flex saves you 26 CHF.

Assuming you will be taking the Glacier Express from Zermatt to St Moritz. Neither the Travel Pass nor the Half Fare Card save you anything on the reservation fee.

Edit, A minor point, the STP covers you completely from Chamonix Mont Blanc station to Zermatt. A short stretch, from Chamonix to Vallorcine is in France, so is not covered by the Half Fare Card. That portion costs 9.70 EUR, about 10 CHF.

With a Half-Fare Card, Saver Day Pass (2 class) can cost as little as 29 (but just a few tickets, on winter/fall, on weekdays). It is more common then to find them at 39.