Maybe it just comes down to Pine's take on Kirk: he seemed too blase about it. Shatner's Kirk (especially in his first season prime) could have sold the grim necessity of it.
In fairness to Pine, he was given the task of playing Kirk on his first space assignment, cocky and untempered by experience, whereas Shatner's Kirk was played as an experienced veteran who had seen the wonders and horrors of space up close for years.
On that first day Kirk had to deal with an enemy/threat who:
Was from 129 years in the future.
Had advanced weaponry and technology.
Had already destroyed a plant and killed it's 6 billion inhabitants.
Had destroyed 5 starfleet ships.
I don't think Shatner Kirk had to deal with anything matching such scope and magnitude. The closest things I can think of would be The Doomsday Machine, and the events of TUC.
Pine Kirk made a judgment call to permanently end the threat Nero posed. That's his responsibility as a captain. Pine Kirk did extend an olive branch before destroying the Narada and Nero smacked his hand away. Despite all Nero had done; including kill his (James T. Kirk's) father. Pine Kirk was attempting to find peace with the Romulans.
Shatner Kirk had no qualms about firing on General Chang's ship in TUC. He didn't treat Khan and his people on the Reliant with kid gloves either. All the shots to area surrounding Reliant's bridge affirm that. Then there are all the Klingons Kirk killed in TSFS. By self-destruct of the Enterprise and by kicking them off a cliff in to a river of lava.
No matter the universe.
KIRK GIVES NO QUARTER TO THOSE WHO CROSS HIM.