The Hades completely outclasses anything outside the Colossus built by the GTVA.
It doesn't. It's just a really big ship. It doesn't neccisarely have any advantages beyond being a big ship (Which is the same problem the colossus has). It should be noted that the Hades was brought down by fighters alone, on its first deployment.
When considering things built by the GTVA, you should also consider the armanent: The GTVA was able to put beam cannons on all of its capital ships. You'd have to consider if the GTI could do the same, as the GTVA had acccess to GTI records (they just didn't decide to use the talking-to-shivans bits, as per bosch), and the GTVA has at least double the scientists as the GTI would have (since they're not sidelining the Vasudans*).
For your question, minute for minute, I think the willing worker is the more productive worker. But the willing worker working a normal work week would be outstripped by the slave worker working dawn to dusk 24/7. Before you even get to the reduced costs of said workers.
So this is
provably false. The more you make people work, the less results you get. Fatigue is a real thing that you can't just beat out of people.
* And if we're going to back to the Nazi point:
The nazis lost a bunch of their scientists by sidelining them. The self-imposed brain drain of authoritarian governments is very real.