The Swiss Travel Pass covers buses to Vaduz while the Eurail pass for multiple countries does not (but it covers trains that pass through). Rick went to Liechtenstein for this TV show so that you wouldn't have to: https://www.ricksteves.com/watch-read-listen/video/tv-show/little-europe.
See a summary of how the pass coverage varies at https://www.ricksteves.com/travel-tips/transportation/trains/switzerland-rail-passes. Both passes have choices for different numbers of travel days, some to use consecutively and some within a month or two, so the timing of these different trips affects the pass prices and options. You may possibly do a lot of math and still come out with similar total expenditures, after adding in extra tickets with either pass.
The Swiss Travel Pass covers more mountain trains and lifts, and museums and in-city transport, but only on your counted rail pass travel days, with no discounts or coverage in between if you have the flexi version of that pass. Would your time in Switzerland fit the confines of a pass for 8 consecutive days at $420 per adult? If so, that might be your pass choice. (The Swiss Travel Pass flexi version for 4 days within a month at $324 covers much less and if that's what you were looking at, then I'd prefer the Global pass, as below).
The Eurail Global Pass covers the Austrian trains as well, is competitively priced, and mountain transport discounts don't require using a travel day on a flexi pass. The version for 10 travel days within 2 months currently costs $407 per adult, with a 10% discount that must be booked by 5 p.m. ET tomorrow. (Prices are subject to change at any time and this may not be the last promotion of the year.)
The separate Austria Eurail Pass for 4 travel days at (currently) $176 just breaks even with buying tickets as you go at the full 2nd-class price.