The leading fanon explanation seems to be along these lines: the original universe Constitution Class was scrapped or never started, due to the "holy crap the Romulans have what?!" reaction to the Narada-Kelvin incident. Then the "New Federation Heavy Cruiser" project was re-started years later, after the engineers had time to design and submit a new proposal. (If you look back to Pentagon weapon programs in the Cold War, there is plenty of RL precedent for this kind of thing - The Soviet Typhoon class strategic missile submarine, for instance, caused a lot of panic in the U.S. Navy at the time it was revealed.)
Since the movie tie-in materials still call Big-E a Constitution Class vessel - and it's highly unlikely they will want to change this - we might assume that the Constitution (NCC-1700?) was for all intents and purposes a prototype, and the Enterprise was the second in her class.