Khan initiated the fight unnecessarily. JLP reacted defensively to events beyond his control.
Picard's was a defensive rage. The Borg attacked once again, and he was finally backed into the last corner where he couldn't take it anymore. Given the stakes, one more retreat was not acceptable.
Khan's was an aggressive rage. Kirk wasn't an immediate threat, but he sought out and then launched a surprise attack on the Enterprise. He could have taken the Reliant and zoomed off into seclusion. Instead, he hunted Kirk.
Only superficially is there a parallel motivation. The historical contexts and the events surrounding the decision making processes for the two individuals are different.