I hate this debate it is so circumstantial and totally depends on the person and situation.
Here: He's in a worse position, so he'll be more motivated.
Again an assumption which is totally person and situational.
Kill a homeless man's family, he has nothing to lose, he cries and is sad all day. Very dangerous. Kill a homeless man's family, he is motivated to kill you and does everything in his power(limited) to get to you and kill you no matter what the cost.
A dictator is going to be overthrown by his people, he is conscious and tries to maintain power and due to the consciousness he loses to the rebellion. A dictator is going to be overthrown by his people, he understands the gravity of the situation and deals with it ruthlessly putting it down.
I just wanted to illustrate that these have to be more concrete situations, but Ceteris paribus I give it to the man with the most resources to his disposal, since it is pointless to generalize hypothetical personalities.
As for some art of war: From the nine situations (23) Soldiers when in desperate straits lose the sense of fear. If there is no place of refuge, they will stand firm. If they are in hostile country, they will show a stubborn front. If there is no help for it,
they will fight hard.
(22 also is similar)
Also I don't think your quote is real. The cornered escape quote is there but not this one. (I think)
It all boils down to if the man with everything to lose realizes he has everything to lose and act accordingly, and I would argue that even if he does not act with the proper vigilance his resources would overman the man with nothing in most cases.