The JJ films have tended to reinforce the idea that there wasn't anything really special about the Enterprise...
I definitely missed this part in the Abramsverse films. The crew aren't as attached to the Enterprise yet, but the ship is only a year old.
Plus, she was called the newest flagship at the beginning of the first film. I'd call that special.
Yep it's supposed to be the most advanced and newest ship in the fleet.