The one scene that plays badly is the final meeting in Pike's quarters between Pike and Kirk. The tone is off - a little too jocular "What a fucking day at the office, huh?" for the losses they've incurred just hours before (at most). And then Kirk sticks the knife in - "You know what, if you'd done things differently to begin with, maybe this situation wouldn't have gone all to shit." That was all a bit jarring and inappropriate.
I agree that the tone wasn't right at the end. The Federation is now at war, and they're shooting the breeze like they just went through a bad simulation together. And there was no sense of loss for the Romulan commander either, something that was a key part of
Balance of Terror. The words were there, but none of the emotion.
But Kirk sticking in the knife does seem on point to me. He never was one to pull his punches -- especially with other starship commanders, for whom he always showed respect and even reverence. I don't think he was trying to say "I told you so" to be petty; but rather to make sure the point wasn't lost that sometimes aggression is the appropriate response. He wasn't going disrespect Captain Pike by tiptoeing around that; nor was he going to let a weaker viewpoint prevail now that war had been declared.
Inappropriate and also avoiding blame. It was SNW-Kirk that caused the Enterprise to be damaged and unable to finish off the Romulan Bird of Prey which led Pike to offer a temporary truce. Unlike TOS-Kirk, SNW-Kirk charged right into the plasma bolt necessitating Pike to move into rescue the Farragut crew. TOS-Kirk backed off and warped away from the plasma bolt instead of trying to go head-to-head with the Romulan.
I wouldn't be so fast to give TOS-Kirk a pass... The reason he chose to warp away was because there was, just moments before, a phaser circuit burnout. The Enterprise was defenseless. And when the BOP decloaked to fire, there really wasn't another option available.
SNW-Kirk had an undamaged ship, an opportunity to strike, and backup right there. He had more options and less time. His biggest miscalculation was that Pike wouldn't press the advantage, and he seemed a good bit annoyed at having to waste time ordering Pike to fire phasers -- and having to justify the direction -- at the end of the scene.
But you're right; blame should go to both. They clearly weren't on the same page at all and that lack of understanding and teamwork made a tense situation dire.