Which one of these two top of the mountain trips is best?
They're both first class attractions and if you have the time and money you should do both. The Schiltorn is mostly a mountain-top panorama attraction, Jungfrau is mostly an engineering marvel/glacier experience. If had to choose just one it would be Jungfrau. While it takes longer to get to the top and is more expensive, it also has more to do. In addition to the commanding views of the glacier valley at the very top, you can also walk on the glacier where their are activities like a zip-line and mini-luge. Then you can take the elevator down and walk inside that glacier and explore the ice-gallery, the network of tunnels in the complex also have lots of exihibts about the region. Hard to put into words but Jungfrau seems more "Mount Everest" to me.
Laurie, Which attraction is "best" is somewhat subjective and a matter of opinion. I definitely agree with Michael's comments that both are absolutely worth seeing if you have the time and money. What time of year will you be there? Of the two, the Jungfraujoch is more expensive and comes with a degree of uncertainty. If the weather is inclement at the top, there won't be any touring out on the glacier. However, even in bad weather it's still possible to tour the Ice Palace and other exhibits, have lunch in one of the pricey restaurants or do some shopping for Swiss goods in one of the shops. The Jungfraujoch is a unique location, as it's constructed mostly inside the mountain, with construction starting in 1896 without the modern tools and equipment that we have today. The Schilthorn is also a great trip and is quicker, cheaper and easier to reach than the Jungfraujoch (especially if you're staying in Mürren). One of it's best features is the revolving restaurant, where visitors can enjoy a fine hot meal with a glass of Vino or a "cool one", while watching the panorama of the Eiger, Monch & Jungfrau glide by the window. The James Bond movie On Her Majesty's Secret Service was filmed at the Schilthorn a number of years ago, so there's also a James Bond Bar one floor below the restaurant, where visitors can enjoy a "Martini shaken not stirred". I believe there's an anniversary of the movie being celebrated there this year, which will be attended by George Lazenby. If you can only visit one, you'll have to make a choice based on which site interests you the most, and which one fits your budget better. Happy travels!
A few more differences: The Jungfrau trip is about double the cost of the Schilthorn. It also takes more time the ascent from Lauterbrunnen to the Jungfraujoch takes almost 2 hours (1:48), of which some 40 minutes are in a dark tunnel bored through the Eiger. They do stop the train once so you can get out and look out the " windows" carved in the rock. The trains can be very crowded. The ride to the Achilthorn is something of a thrill in itself, as you dangle from a cable high above the ground. Great views the whole time and it is pretty fast. Once you arrive, there is much more to do at the Jungfraujoch. We really like the ice palace and carvings when it isn't crowded. Outside, you can play in the snow (platters for sliding, mostly for kids), enjoy the views down the Konkordiaplatz to the Eggishorn, or walk to the Mönchshütte on a marked path across the snow. The inside of the main building at Jungfraujoch is generally crowded and food prices are high, so be prepared with your own food and beverages if you are not walking to the hut ( definitely plan to buy food or beverage there if you go, as that is part of the experience).
I loved the Schilthorn. Much less expensive to reach and the views are totally amazing. There was even WiFi where I phoned my Mom via Facetime. it was incredibly cool.
I have heard that the Jungfrau is more of a glacier view with things to do atop the glacier whereas the Schilthorn gives you more mountain range views. I was completely satisfied with my trip atop the Piz Gloria. They even have the James Bond music playing while you ride the cable car to the top.
I would do the Jungfraujoch. The Schilthorn has great views, but is similar to "cable car rides with glorious mountain views" that are found many places. I found the Jungfraujoch to be a more unique experience. Of course, this is my opinion...but you did ask so I obliged. The good news is that you will have a great time whichever you choose.