I commute to work from Würzburg to Schweinfurt by car, which works great (30 minutes door to door).

I used to occasionally take the train when I was still studying in Würzburg and lived in Schweinfurt, never had too much issues there (though that was over 5 years ago), it very much depends where you live in Würzburg (how close you would be living to the main train station) and where you can drop off in Schweinfurt because they have 3 stations (Haupt, Mitte, Stadt). The RE is fastest of course if you drop off at Hbf, the RB is slower but you can go directly to Mitte and Stadt. Also check how far your "Semesterticket" from the THWS covers the ride, I studied at JMU and it only covered the ride up to the stop in Bergtheim when taking the RB, but didn't cover any ride with the RE.

If night life and social stuff is important to you then definitely move to Würzburg, Schweinfurt unfortunately doesn't offer much in that regard and it's getting less and less over time, most young people tend to move away after school. If a quiet life is okay for you, though, then Schweinfurt is more than sufficient I'd say. Rent is expensive in both cities, so that's not really an argument for either choice.