Yeah, Jellico is probably more hard ass than Picard, but what we saw on the Enterprise could have been him exaggerating his personality.
If anything, I think the plot exaggerated his personality to provide conflict. What's funny is that the conflict generated by his personality just made the Enterprise
crew look bad, as though Picard coddled them.
Interesting idea about him playing it up, but I think if he were consciously putting on an act, he would have mended things with Riker after the crisis. Instead they still hate each other, even when he's forced to ask for Riker's help. His dislike for Riker must be real at the very least.
Their dislike was genuine. I think that was the point of them dropping the ranks during their discussion. But Jellico was big enough to ask for Riker's help, something he didn't need to do. LaForge could've flown the shuttle. Riker acted like an ass (again), almost taunting Jellico when he said, "Then ask me." He enjoyed that moment too much for someone who'd been relieved of duty because he couldn't follow his captain's orders.