Similar? Yes. A word-for-word rip off with the lines switched? No. But the same people in a similar situation will likely say similar things.
Wrath of Khan
SPOCK: The ship... out of danger?
KIRK: How's our ship?
SPOCK: Out of danger.
I think Scotty saying McCoy's exact "You'd better get down here... better hurry" at the start was a little too much. Although the bit about not opening the door for fear of flooding the compartment with radiation sounds like they're both quoting from a safety manual, which any crewman would know by heart.
I think the new scene works wonderfully on several levels - as a touching scene, the resolution of Spock's story arc, and as an alternate universe version of one of Trek's most famous moments for longtime fans. It seems that, along with the Enterprise-D's warp core being breached by a Klingon Bird-of-Prey in "Yesterday's Enterprise" and Star Trek: Generations
and Kes or Seven scanning that Krenim torpedo lodged in the Jeffries' Tube in "Before and After"/"Year of Hell", somone was gonna die in engineering in an epic encounter with Khan, whatever the timeline.
You know what bugs me about the Into Darkness
scene? I caught it on my second viewing and can't unsee: Spock's hand, when Kirk's falls in close-up it's doing the Vulcan salute against the glass, and they cut to another angle with his fingers widely spread. Annoying!