IMHO:
Jimmy was disloyal. This is ultimately why he was killed. Nuck stood in front of him and said "I'm going to ruin you all". He has always done what he says. He even said so right before that line IIRC.
Eli was spared for two reasons: 1. He is Nuck's brother. Nuck himself said "blood is thicker than water". 2. Now that Nuck has beaten the federal rap and re-established his position as ruler of AC, and especially with the exhibition of his control over Eli vis-a-vis his plea deal and the taking care of Eli's family in the interim, he thinks he has complete control over Eli.
I'm not convinced he believed Eli over Jimmy regarding the hit. It seems he had already made his decisions when he went to talk thing over with Eli on the porch. He seemed like he felt Eli was lying anyway.
I quite like the Nucky character. He is starting to seem much more ruthless than he was in the first season. Previously, he seemed more like a businessman only, leaving gruesome details to others. However, killing Jimmy himself and then being able to lie about it so seemingly convincingly the next morning makes me think he is entirely cold-blooded and we have been fooled almost as much as Margaret has.