If you're talking about Kirk with Nero, where was it ever shown that he was proud of killing him? And again, I have to point out that the idea that Nero was "dying" is pure speculation. He could have been traversing the wormhole to another universe in his still very dangerous even without the red matter ship for all we know.
I don't think Nero would be much of a threat since he fired all his weapons ("Fire EVERYTHING!"), his ship is literally cut in half (One half is spinning in the opposite direction of the other) and his crew are fleeing away from their stations in utter panic. Bonus points! Even in the commentary track they said that the black hole was going to kill Nero. Also, these lines.
Kirk: Your ship is compromised. Too close to the anomaly to survive without assistance which we are willing to provide.
And that line delivery "You've got it. Arm phasers. Fire everything we've got." and Sulu's "Yes sir!" smirk definitely gives the impression that they're happy about having the chance to kill Nero themselves.