Watching it now, I'd describe the differences between Bush and Thatcher as largely stylistic. When she talked, Thatcher always sounded like a hammer pounding a nail. Bush sounded tentative even when his words were emphatic. Watching it then, I remember thinking, "She's giving him the backbone to go to war."
That, apparently, was also Thatcher's impression. She later recalled what she'd advised Bush privately. "Indeed I told him that aggressors must be stopped, not only stopped, but they must be thrown out. An aggressor cannot gain from his aggression. He must be thrown out and really, by that time in my mind, I thought we ought to throw him out so decisively that he could never think of doing it again."
Or as she told Bush a few days later, "Remember, George, this is no time to go wobbly."
It's interesting that Thatcher, in Aspen, talked of teaching Hussein a lesson, not driving him out of power in Iraq. When Bush ended the Gulf War with Kuwait liberated but Baghdad uninvaded and Hussein still in charge there, he was criticized for not finishing the job he'd started. If he'd sounded more bellicose at the get-go, if he'd out-Thatchered Thatcher at Aspen, maybe he'd have gotten the benefit of the doubt.
Bush enjoyed repeating the advice Thatcher had given him—don't go wobbly. I wonder if his son, George W., ever thought it was funny. George W.'s fixation on invading Iraq in 2003 is more easily explained in terms of family honor than faulty intelligence. According to Bob Woodward, W. didn't ask for his father's counsel or blessing. "You know he is the wrong father to appeal to in terms of strength," said the son. "There is a higher father that I appeal to."