First we stick a cat in a box...

OK, so can someone explain to me the difference between these two scenarios:
1 - we do Schroedinger's cat experiment.
2 - we stick a dude in a box with a coin, a cat, and a club, and he kills the fucking cat if the coin flip comes up heads.

Assume that there's no way for information to get out of the box until we actually open it and look inside.  In either situation, it seems to me that we've got a 50/50 chance when we open the box of seeing a live versus a dead cat.  After the magic moment has passed (one half-life or the dude's flipped the coin), we've got either a dead cat or a live cat, not like 50% of a live cat, we just don't (can't) know which until we actually look.

I've seen people arguing that setup (1) is different because of QUANTUMS, but I've never had it adequately explained to me how a random quantum event is different from any other random event.

This doesn't really answer your question, but one difference is that with radiation, the sample may not decay at a steady rate.  Say the half-life of a sample is 30 days.  After 29 days, it's possible (though extremely unlikely) that the sample has not decayed at all, and half of it will decay in the last second of those 30 days.  Half-life is an average, not a set rate.

Again, I'm pretty sure this doesn't answer your question, but maybe someone who's had more physics can take it from there.