Or...
Maybe it's because Mufasa was dangerously close to slipping right before Scar grabbed hold of him lol. He had to dig his claws in real deep in order to keep him from falling backwards.
Simba on the other hand had a more solid grip, so Scar got to ease his hold on his paws a little.
The first scene also seemed more urgent since Scar knew he'd have to let go quickly before the stampede was over or someone else saw, so perhaps some of the tension and anxiety he felt fueled his iron grip. Scar was less stressed in Simba's situation since he knew he was in no major hurry to finish him off, so his hold was much more relaxed.
As Moka pointed out, it's also a fact that Scar hated Mufasa more than he hated Simba. Whatever hatred he felt towards Simba was directly related to that of Mufasa, so it's only natural that he tried to cause his brother more physical pain.
Sorry, I'm not trying to outsmart anyone here.
I just have a lot to say on this subject.