At least in terms of goofiness the new movie seems to be very much like TOS, even more so than TFF. But there is something fishy about this idea.
I couldn't put my finger on it until now and I think that the concept of virtue might provide some insights.
Let's approach the issue first via the humour and then via the three main characters.
TOS is often funny and virtually all of the folks, except for perhaps Sulu and Uhura, frequently fool around. They enjoy their company, ease their daily troubles but basically they are all serious, hard-working folks.
In ST09 on the other hand you get more self-ridiculing humour. The postmodern kind of eternally self-reflexive, relativizing big puff. We don't just try to have a good time during our long days but it's all just a game.
That's an easy but not a virtuous way to deal with the troubles of life. Scotty's jokes are perhaps the best example of this kind of humour and it is worthwhile to point out that the old Scotty was usually involuntarily funny (except when he drank Scotch or got written and directed to bump into a bulkhead by Shatner) precisely when he was deadly serious.
McCoy is his cranky old self and due to Urban's brilliant performance there are no apparent differences. If you have just seen the movies and a few random TOS episodes you could easily get the impression that he is just an ill-tempered old guy. But from time to time we see how much he really cares about his patients and his friends. Beneath his bickering with Spock their deep friendship only appears a few times.
As McCoy's warm side has appeared so infrequently it's not a big deal that we haven't seen it in ST09. That's indeed true but NuMcCoy has gone through some trouble in his life which makes it seem as if he is cranky precisely because of that. The acting was top notch but the writing changes the temperamental but warm old country doctor into a cranky and cynical young man.
Kirk has experienced fascist horrors on Tarsus IV in his youth, bullying in the Academy and failure when he faced the vampire cloud on the Farragut as young ensign. Despite of that he turned into a thoughtful and self-doubting but at the same time playful and confident young captain.
NuKirk has gone through similar experiences. Too much and wrong order on Tarsus IV now became too much and wrong order at home, he got bullied by other Starfleet cadets even before he entered the Academy and he also faced failure when he cheated during the Kobayashi Maru test and was reprimanded for it. So like his first version he faces nasty order (Tarsus IV, evil stepfather) as well as nasty chaos (bullying, personal failure) but instead of balancing them wisely he just becomes the stereotypical adolescent who rejects order and enjoys chaos.
Spock who is even more so than Kirk in an eternal struggle between chaos and order chose his Vulcan side. The main theme in TOS is that his human side is lurking underneath the surface and that Spock is more human than he admits. This is most clearly visible in This Side of Paradise and Amok Time. His saga ends in TUC, Unification and ST09 with him accepting his human side openly.
While Spock joined Starfleet in order to secretly explore and embrace his human side (that's precisely why he is so uber-Vulcan in TOS) EmoSpock did it in order to flip off the racist Vulcan establishment. Mummy was insulted so he has to indirectly defend her. With mummy being the main reason he is in Starfleet he consequently goes nuts when she dies (which would also have impacted Spock but not so strongly) and he is later encouraged to continue along this path of being an unorthodox, more relaxed type of Vulcan by Sarek as well as his future self. The consequences of this ill advise to continue to be EmoSpock are clearly visible when he calmly tells Kirk that he yearns to avenge the death of mummy.
On the surface it appears that there is not much difference, after all the balanced old Spock gives his younger self the advise to be like him. Yet Spock's happy state is the result of a life-long struggle from discipline to slowly letting it go and realizing that it is possible. He can't reveal the end result to his younger self without telling him about the path that let to that goal.
Same with Sarek, he can't tell Spock to not suppress his emotions because his beautiful admission that he has loved Amanda (as if Spock hadn't known that) gets perverted into an injunction to let the inner Romulan out.
Spock slowly allowed himself to let his guard down and create some space for intuition, gut-feeling and love whereas EmoSpock allows himself quickly to do whatever the hell he wants to.
All three main characters have one thing in common, they are virtuous people. Not necessarily heroes, in the case of McCoy not even special but precisely that, being just a good old country doctor, makes McCoy so grand.
The second versions of these characters which were truly fantastically played on the other hand all lack virtue. This doesn't mean that they are vicious or wicked, that they do bad work or that they aren't capable of heroic deeds. After all Spock and Kirk did gamble with their life when they went on the Narada. But all the big heroics can't substitute the emptiness in their hearts which are filled with cynicism and despair, adolescent arrogance, reveling in your own emotions ... but not virtues.
It's not easy to be a virtuous person, I personally don't think I am one so this is not meant to be some moral superiority game. It's perhaps not even a writing issue but indicative of these materialistic and cynical times that fictional characters adapt these qualities.
I am perhaps simple-minded and unhip but I mainly enjoy Trek because it features good people who do good things for good reasons.
So I hope that this doesn't get misread as a hateful bashing of a movie which I truly enjoyed but as a mourning of things that got lost.