Train or Plane from Interlaken to Salzburg?

Your research is pretty much right on, however when comparing times and prices be sure to add the 2 hr train from Interlaken to Zurich and the 1-2 hrs you need to be at the Zurich airport before the flight. It may very well still be quicker and/or less expensive to fly but be sure you are comparing apples to apples.

I also think that train fare may be the last minute full charge fare - there may be cheaper fares purchased ahead of time.

It is 2 hours and 15 minutes by train from Interlaken Ost to Zurich airport, you should be there 2 hours before flight time, 3 hours 30 minutes flight, changing planes in Duesseldorf, then another 45 minutes to get luggage and get to central Salzburg, I count 8 1/2 hours. And that is 151 CHF, not USD.
By rail, it is 7 1/2 hours by train. Advance purchase ticket can be had for 72 CHF, same purchase and restrictions of an airline ticket, and 166 CHF for a fully refundable, flexible ticket.
Train seems to be the better option, considering lack of stress, get up and walk around anytime you want, bar/restaurant car, etc.

Thanks Sam for clarifying that. Personally I would have opted for the train anyway - I hate the whole getting to the airport, having to wait for the flight, changing planes, etc etc etc.

Thank you, Nancy and Sam, for your replies - much appreciated! Do I need a eurail pass for train travel from Interlaken to Salzburg or will a point-to-point ticket be okay? We also plan to do a day trip to Berchetengaden and then take the train to Munich, where we also plan to do day trips to Dachau and Neuschweanstein castle. Is a 3-country eurail pass the way to go?

Eurail passes are almost never a good financial choice nowadays unless you are doing a huge amount of long distance travel. Your only long-distance trip is from Interlaken to Salzburg. This probably will be cheaper if booked in advance - Your $240 price is probably the immediate-travel one, you should be able to find something much cheaper online from www.sbb.ch. Tickets go on sale about three months in advance, and I got quoted a single fare for 3rd July of CHF72, which is roughly the same in dollars.

For Salzburg to Berchtesgarten, the German rail planner site at bahn.de recommends using a bus route 840 rather than the less direct rail route. No fare is quoted but I'd be surprised if it was over 20 euros and probably less.

From Salzburg to Munich and Munich to Fuessen (for Neuschwanstein) you can use a Bayern Card one-day pass which is 23 euros per person, with significant discounts on the second and later passes if you buy for a group of people. This gives unlimited travel for one day on all trains in Bavaria and over the border to Salzburg, with the exception of the highest-level ICE/IC/EC/RJ expresses, as well as almost all city and rural buses, trams and subways. Between Salzburg and Munich the expresses don't run any faster than the limited-stop local trains, and between Munich and Fuessen there are only local trains anyway.

Dachau is within the Munich urban transport ticketing scheme, so that won't be very expensive.

Yes the 72 CHF/p price I quoted was from www.sbb.ch/en. You can buy the tickets now on-line and print the tickets at home. The price will increase the closer you get to your travel date.

The Bayern ticket is 23 EUR for the first person and 5 euro for each additional person for up to 5 people travelling together. You buy them from a vending machine in Salzburg train station. They cost an additional 2 EUR to buy them at the ticket window. There is a slightly less expensive version called the Guten Tag ticket, but with the Bayern ticket, you can use the U-bahn, S-bahn, trams in Munich for the rest of the day.
You can also use the Bayern ticket for a day trip to Fuessen, again after 9 am weekdays. For a day trip to Dachau, use a Munich XXL group day ticket (assuming you are traveling with others).

"it will take over 8 hours by train and approximately $240 one way."

If you purchase rail tickets well in advance, which I'm sure you will have to do to get a good air fare, you can get tickets from Interlaken to Salzburg from German Rail for as low as 49 euro ($55). It will still take 8 hours.

But compare the train from Zürich to the plane from Zurich, you can get rail tickets from German Rail for Zürich to Salzurg for 39€ ($44), compared to $150 for flying.

Thank you all for the information - they're very helpful!