I always thought Jellico wasn't that bad of a guy. Every time he was introduced to someone in that episode he was cordial to them for example. His command style definitely was "his way or the highway" and he was a micro manager. That's not bad, it's just different. Especially when everyone's been serving under Picard who basically gives his people all the leeway in the world so long as the job gets done.
Jellico to me seemed to put the mission before the people. Which is a very military attitude. To him they were facing the prospect of war if things went wrong. Jellico said as much to Picard and Troi. It wasn't that he didn't care about the people under his command, but he couldn't baby them at the expense of the mission. To Riker, Jellico was willing to sacrifice Picard to further the mission. He wasn't wrong. To Jellico, Picard is a small thing compared to the prospect of preventing a war, which was his mission.
Riker was insubordinate to Jellico and was increasingly so as things progressed. Jellico felt that was a danger to the mission having someone he couldn't rely upon in a critical position. So yes, when Riker crossed the line, he's relieved and Data's in the red shirt. Frankly Riker wasn't very professional in the episode at all. To me the scene between Geordi and Jellico in the shuttle was very telling. Not only did it demonstrate Jellico did attempt to bond with his people when given the chance, but that he'll put the mission ahead of personal concerns.
He did drop his pride when he asked Riker to pilot the mission. Why? His pride is a small thing to the success of the mission. I think he "dropped the ranks" and ripped into Riker, just to give Riker the chance to get all the nasty things he wanted to say to Jellico off his chest, so he'd perform the mission all the better. To say nothing about once the mission was a success and Jellico had the upper hand, he immediately demanded Picard's return. So you really can't say he didn't care about the people under his command, even if he didn't have time to pamper them so to say.
I suppose I ranted a bit on this, but he is one of my favorite characters and really did shake things up nicely on the TNG set. To me, Jellico was the professional, get the mission done, no matter the cost type of man. Just the sort of person you'd want on a high stakes mission where the threat of war is imminent. His style was different, and admittedly overbearing, but that doesn't mean it was wrong.