Why did Tyrion survive while Ned died in Game of Thrones?
They were in a similar situation, I tried to do the comparison on a quite superficial level:
Ned was accused of plotting to assassinate the king and treason, while Tyrion was accused of directly poisoning the king.
Although Sansa was not as helpful as Jaime, she still managed to get a promise of mercy. The disadvantage on Ned was the man in charge was Joffrey in stead of a more reasonable Tywin. However, he has a son marching south with 20,000 men and Jaime as hostage, which should give him way stronger bargain power.
But there must be deeper level reasons behind it. So what lead to their different endings? Or maybe Ned was just unlucky?