And here NuKirk decides to destroy an enemy ship that was already dying. That's not heroic, and it's not why I liked classic Kirk in the first place.
I mentioned this on another thread actually. In WWII the Nazis were commanded to kill survivors of damaged ships towards the end of the war when their position started to look dicey. What Kirk and Spock do here is very similar, except they're doing it for personal satisfaction rather than orders so one could argue that their motives are more reprehensible.
They have transporters, they have a brig, and if the Narada's shields are down they can TRY to beam her crew off in accordance with standard protocols for a ship in distress. Instead they opt to murder them! I find it extremely disturbing that I am supposed to admire murderers - that is to say they are not acting in self defence when they fire, their sensors tell them the ship is no threat, and that the ship is being destroyed. They do not even know for sure if there are children on board (the Narada has female crew and they've had 25 years in which to breed).
Inglorious Basterds and NuBattlestar Galactica toyed with American double standards knowingly, so those who aren't self aware enough to spot the double-standard can applaud the heroes, while those who are slightly more morally evolved (seen as left-wing attitudes in some circles) can shake their heads and tut at the hypocrisy of humanity.
In NuTrek Kirk is promoted to command his own ship. This is one of the reasons why I felt Kirk wasn't ready for command. He clearly bases his decisions on his own personal feelings rather than Starfleets rules - that makes him a ticking time bomb!