I haven't been to Switzerland, but I'm going in September and so have been researching this.
The Half Fare Card (per Rick's page on it) "Gives you 50 percent off on all Swiss trains (including private railways and high-mountain routes, including the Jungfraujoch), postal buses, city trams and buses, mountain lifts, and lake and river boats within a one-month span." That's it. But it's only 120 CHF. So, if your trips would add up to more than 240 CHF at full fare, you would save money with this.
The Swiss Pass completely covers almost all "lowland" transit (things that are not high mountain lifts or special scenic trains like the Glacier Express). That includes trains (regional and long distance), postal buses, local buses and metros in cities, and boats. It does cover most of the cost of the scenic trains, but you have to add mandatory reservation fees (or you can take regular trains on the same routes, fully covered by the Swiss Pass). It also gets you 50% off most high mountain lifts (only 25% off the Jungfraujoch train, while the Half Fare Card gets you 50% off this very expensive ride). It also acts as a museum pass (free entry to many museums all over the country; only half off the expensive Swiss Transit Museum in Luzern).
Of course, the Swiss Pass costs much more than 120 CHF. So figuring out whether it will save money is harder. But there's also a convenience factor. For any ride that's fully covered, you don't have to buy tickets; you just flash your pass. With a Half Fare Card, you still have to buy tickets every time. And there's the peace of mind of knowing that if you decide to take more trips (like going up Mt. Rigi in addition to Mt. Pilatus while in Luzern) or if you see an extra museum because of a rainy day, it's mostly or completely already paid for.
As Sam said, remember that the default price shown on the Swiss Rail website is with a Half Fare Card; you have to go a couple of screens in to see the price without a card.
Here's Rick's Switzerland pass page with more information: http://www.ricksteves.com/travel-tips/transportation/trains/switzerland-rail-passes