This thing rhymes with the Allais paradox, and my loss-aversion based resolution applies here also. In Case 2, I imagine myself being the dumb cheapskate who could have avoided death if only he was a bit more generous. In Case 1, I have to face death either way, and I see myself as a victim, not as a bargainer. And this is perfectly rational, because this is exactly how people will later think about my situation.

Basically, the extra term in my utility function that resolves the paradox is the same that makes me prefer to die in an accident that's someone else's fault, as opposed to my fault.

By the way, I would pay all the money I have, in both cases, so I guess there is something wrong with this exact formulation of the question.