This  covers most of it: Soleimani Killing Makes no Difference; Politics Muddys; Remember Pearl Harbor.

If an individual embodies an ideology, a system, or a non-transferable web of control, then assassination, death, or removal from power can potentially change the course of history.  Examples:

• Hitler is preeminent in  cult of personality,  the then-extant oath of personal loyalty to the “fuhrer”, nontransferably embodied in a unique individual.
• Stalin, who ranks close behind, survived by devouring his subordinates; many think he was assassinated by Beria.
• Hirohito, embodiment of the divine, whose position in postwar Japan was preserved by MacArthur to facilitate governance.
• Countless cult leaders, scaling in size from Charles Manson to David Koresh to Jim Jones to Father Charles Coughlin.
• Osama bin Laden is a special case. His liquidation was effective, for particular reasons you may ponder.

Cases that made little or no difference:

• Qasem Soleimani.
• F.D.R., whose death occurred late in the war, long  after isolationism restrained U.S. commitment.
• J.F.K., disputed by those who argue he would have withdrawn  U.S. forces from Vietnam.
• Martin Luther King, whose martyrdom could not halt the tide of civil rights.
• Abraham Lincoln; who many polls identify as the most widely admired person in the world.

Various megachurch preachers straddle the line.  Some terrorist leaders are irreplaceable, while others are not. An attempt to distill a simple rule can be frustrating. Cults of personality are simple. Other cases are more complex. In some societies or groupings, it is possible for the image of a public figure to be broadly delegated, along with principles and causes. In other societies, the mission or cause is  is inextricably embodied in the living individual. Or the image could be a role, interchangeably filled by many aspiring actors. See Baghdadi Dead; the Role Looking for an Actor.

Iran, Hezbollah, and Hamas are not characterized by cults of personality or acting jobs. Broad delegation is fostered, which implies that assassinations cannot cause  functional change.

It pays to know the difference, if you can figure it out.