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.