Well, the size of the Enterprise IS important.
I say that as someone who really liked the JJ-movies:
The size of starships in the JJverse renders a lot of potential stories unusable: We usually see our main characters on away missions, and for battles they only have a handfull of people at disposal. That has to be expected for a smaller ship. The JJprise must have had at least four to five thousand people on it. There is really no need for the captain to beam over to the Narada to save Pike, when they could easily send an army of a few hundred redshirts over.
Likewise transwarp-beaming is seriously limiting story potential: Often, our heroes are captured on a primitive planet, while the Enterprise/Voyager/Defiant is light-years away. In the prime-verse our heroes have to help themselves. In the JJverse, Kirk is captured by Klingons on Kronos, submits a distress call, and is beamed back to earth. No real tension to fill an episode there. One or two movies get around those problems. But if they have to step around those obvious solutions on a weekly basis, audiences will get suspicious, and writers tired, because they have to invent even more technobabble to get around those limitations and put our heroes in harm.
As being said: The new series is probably not trying to reference too much previous history, because that's a frikk'n nightmare in either universe. The only real boundaries is internal consistency ("no beaming through shields!", "Photon torpedoes more powerfull than phasers!", "warp engines for interstellar travel vs. impulse engines for orbit and battle maneuvers"). And, since the JJverse avoided being a clean reboot, those rules are basically identical in both universes. I would even argue the JJverse demands more knowledge of Trek history than the prime universe (You can pretty much dive into TNG, VOY and ENT at the beginning of each without ANY knowledge of any previous series. The JJverse on the other hand requires you to basically know the plots and characters of 30-40 years old television episodes and movies to fully understand into Darkness)
On the other hand a series (veeeery loosely) set in the prime universe allows the guest appearence of lots of Trek guest stars (a Borg episode guest starring Jeri Ryan and LeVar Burton, Admiral Janeway headbutting with the new crew, Quark helping our heroes during an undercover mission). Although that shouldn't be overdone, more in the vain of how Scotty, Spock and Sarek appeared on TNG or Picard on DS9. But it would allow for cross-promotion with the old series (who will try to find new audiences on CBS access, too), while in the JJverse they would basically only be allowed to reference a handfull of movies, and guest appereances would be much more costly (because those are movie-actors) if not downright impossible.
One thing is certain: We will never see the ramifications of the Dominion War or either Romulus or Vulcan being destroyed. While those were huge in-universe events, they are hardly known outside the core fan base.
The logical solution therefore would be an arms-length-reboot. Something that's officially set in the prime universe, but looks and feels like the JJverse. In the same way TNG was officially a continuation of TOS, while in reality it was more of a reboot of the same concept with new characters.
That being said, this would require the producers to actually be clever, and allowing for ambiguity in the setting. Two things Hollywood-producers aren't exactly known for...
