Yet another difference between the two, beside the cost and time to get there: the Schilthorn is a ride in a cablecar high off the ground (spectacular and thrilling, but scary for some), which the train to the Jungfraujoch takes you through a tunnel for 45 minutes of the journey---dark, no views, and claustrophic for some.
If you can handle the cablecar I think the Schilthor makes a much nicer excursion, with hiking and sightseeing opportunities on the way---Grutschalp, Mürren, Gimmelwald, Trummelbach Falls, Lauterbrunnen--that can fill a whole day.
On the day you arrive, after leaving your bags in Interlaken, you could do all but the last section of the Jungfrau route, visiting Kleine Scheidegg by way of Grindelwald and the gondola up to Männlichen, walk to Kleine Scheidegg, and walk or ride the train down to Wengen to look around. There are various restaurants with view decks for lunch up on the Männlichen ridge.
Where do you go from Interlaken on the 22nd? If back to Zürich, you could go by way of the Golden Pass route to Luzern, maybe with one leg of the journey by boat if you have time.