We are trying to see if it's possible to go from Vienna to Prague and backwards the same day.
Yes, it is possible. Travel time between the cities by train is roughly 4:30-5 hours (depending on departure), while first morning train from Vienna to Prague departs at 6:50am (arr. to Czech capital at 11:21), last evening train from Prague to Vienna departs 18:39 (arr. 23:03)
Worth it? Well, it depends a lot on your sightseeing practices. Basically you will have about 7 hours in Prague, theoretically it is enough to see the city center
p.s. at this forum we mainly help out with rail itineraries, but the full picture - one of the bus companies (EuroLines) which operates between Vienna and Prague actually offers 3:55 journeys between the cities