The impression I get is that he watched TOS as a kid when he was too young to understand many of its nuances but he's watched the TOS movies more recently and enjoyed them because of the increased action quotient (and in fairness I think this is important in a movie as opposed to a series). The absence of Chapel and Rand but inclusion of Chekov lends some support to this.
His comprehension of how Starfleet should be organised or what its ideals were meant to represent seem to be very ropey. He seems to have only the most basic grasp of what level of tech existed in TOS or the butterfly effect of changing those parameters. He doesn't seem to understand the way Trek was based on naval tradition or why that mattered.
He seems happy to keep the women in their place though.
Star Trek as a franchise has had numerous series and movies to establish what Trek is. JJ has only had 2 movies to do that.
I think that his stamp is very clear and distinctive and I would not say that the results are bad - they have proved very popular - but I just wish he had injected the same amount of energy without watering down the naval tradition so much and without upgrading the tech (as opposed to the look of the tech) to such a degree. I also wish that he could have taken the bull by the horns and built on the improvements in equality that came out of DS9 and Voyager but he slotted right back into the sexism of the sixties - not in the way the established women are portrayed - they're very good - but in the way that Starfleet is incredibly male-dominated and incredibly human dominated for that matter.