Well, if April had an Enterprise, and his was, I assume, the 300-meter size certain people are so fond of, wouldn't *that* ship be of the Constitution class? Or was there a plaque or sign that says this Enterprise is a Connie? Besides, why would they decommission a class of ship that can only be, at maximum, 30 years old?
Unless technology in the nuUniverse progresses even faster than it did in the prime universe. Actually, considering the Vengeance and her WORKING transwarp drive, not only are they progressing faster, their tech works better.
I like the fact that there is working transwarp in the new films, it opens up a lot more story possibilities.
I am hoping that the year between the capture of Khan and the rechristening of the Enterprise will mean some nice upgrades have been installed. Possibly even transwarp as it has been perfected on the Vengeance, a few of those Bo***ck phaser turrets wouldn't go amiss either.
The tech has already been tested via the Vengeance so no reason not to use them on the Enterprise as it is plenty big enough in this timeline to carry them.