>> I had also been looking at the regional oberland pass but am I correct in thinking that it does not cover Lucerne, Pilatus or Rigi?
Yes. You can see exactly what it covers on the map here:
www.myswissalps.com/re gionalpassberneseoberl and/validity
As explained in the legend on the map, red lines are trains, yellow lines are buses, black lines are cable cars, white lines are boats. Solid lines are free, dotted lines are discounted. Discounts are mostly 50%, but less than that where you see the letter "B" (e.g. from Kleine Scheidegg to the Jungfraujoch).
Grey lines on the map indicate transport that is not covered by the pass. That shows that Pilatus, the Rigi and boats on the Vierwaldstättersee (Lake Lucerne) are not covered. It looks like local transport within Luzern would be covered (e.g. buses), but that would only be useful if your accommodation was not centrally located. Most things within Luzern itself, that are of interest to a tourist, can be easily reached on foot.
>> Does the Swiss travel pass cover most of the mountain transport such as cable car and cogwheel or only some of them?
The Swiss Travel Pass provides a 50% discount on the great majority of cable cars and cogwheel trains, and some are completely free with the pass. A very few are not covered. You can see what is covered, and to what extent, by looking at the validity map, which you can download from here:
>> What is the average cost of cogwheel trains and cable cars?
They differ. Some routes are very short, others quite long. You can find out the cost by going to the website for a particular cable car or cogwheel train, or in some cases by using the Swiss Timetable:
>> Also do the Swiss travel pass and half fare card offer a discount for the Jungfrau tour?
Yes. The Swiss Travel Pass provides free travel as far as Grindelwald or Wengen, and 25% discount between there and the Jungfraujoch. The Swiss Half Fare Card provides 50% discount for the whole trip.
>> I am still undecided between the travel pass or half fare card. The travel pass would offer more freedom and ease but after researching some of the prices of the trains between the different villages I think the half fare card might be more economical.
There's certainly a lot to be said for the convenience and flexibility of the Swiss Travel Pass, but if you definitely want the cheaper option, there is only one way to be sure. That is to add up the cost of every train, bus, boat and cable car trip you will take and compare what that would cost with the Swiss Travel Pass compared with the Swiss Half Fare Card. Arno has already explained above how you can do that.