It is a matter of personality.
Luffy is the kind of person that knows he can rely on his friends. He fought like crazy in thriller bark and then allowed himself to pass out(maybe his subconcious CoO let him know that it is ok to rest, but that's speculation).
Zoro has an almost opposite personality. In his core, Zoro is a loner who is willing to take full responsibility for his own life and safety, this is what he expects from himself.
Over time, since spending time with the strawhats, he learned to trust others more and to have faith in his friends' abilities but when he's left to himself, he is still fully prepared and willing to do the job all by himself.
Luffy's willpower thrives off his friends' motivation. Remember Enies Lobby?
It were Usopp's words of encouragement that kept Luffy going.
I am not saying that Luffy doesn't have his own strength. But in general, he is a very sociable person, he's always in the center of the party, always where the fun and the noise is. The one thing that has the capability to break Luffy is when he is alone.
It has been like this since his childhood, when he ran after Ace and Sabo despite their rejection and initial acts of violence against him.
Being all alone and without friends was worse for Luffy than being injured.
Meanwhile, Zoro is neither a very sociable person nor does he need a lot of company.
Zoro is fine by himself.
What both of them have in common is their willingness to give everything for the sake of their friends. During the Thriller Bark scene in question Zoro knew that the strawhats' safety is now in his hands.
Luffy is the main character in the center of attention.
Zoro is the reliable guy in the background. He doesn't need nor want anyone to cheer him on or to appreciate his sacrifice. The reason he could stand the pain longer than Luffy could is becasue he WANTED it.
