I think also it depends where in the US you are. The laws vary by state. Cic has a good point that intent and the individual scenario make a lot of difference as well. I think you could bend either scenario to where one or the other person would win, depending on the circumstances.
Speaking specifically to the first scenario, there is the concept of "Castle Doctrine":
http://en.wikipedia.org/wiki/Castle_Doctrine
Not every state has this type of law. I know in Texas you are allowed to use deadly force on someone who is illegally trespassing on your property and threatening you. So, in this state, if you broke into my house and I shot you, I would likely have the law on my side - I probably wouldn't even be arrested, regardless of whether you were dead or alive, if the circumstances seemed to indicate that you were trespassing with intent to cause me harm.
In some states, I would have to get as far away as possible and announce in a loud voice that I was prepared to defend myself/property with deadly force before firing.
Of course, that is speaking to intentional harm I would cause a robber. As far as unintentional harm, there is a famous and often mis-cited case in the opposite extreme - of a burglar who fell through a skylight and sued for his injuries. (Accounts of this are likely what lead you to ask this question in the first place)
Ricky Bodine was a 19-year-old high-school graduate who, with three other friends (one of whom had a criminal record), decided the night of March 1, 1982, to steal a floodlight from the roof of the Enterprise High School gymnasium. Ricky climbed the roof, removed the floodlight, lowered it to the ground to his friends, and, as he was walking across the roof (perhaps to steal a second floodlight), he fell through the skylight.
In this case, he sued, and the school settled out of court to avoid paying court costs. This is generally the case that people site when they say 'if someone is injured on your property they can sue and win' - they're partially right, but for the wrong reasons. They often also talk about a knife that the person fell on, and it being a private home, but none of these are part of the actual case. The school settled because even if they won they'd be out court costs, and it was cheaper to settle. There was no decision made regarding whether the thief was actually entitled to the money.