Also there is the canon debate of this comic.
What "canon debate"?
As with all "Star Trek" tie-ins, live-action, onscreen material is canonical. All else may be "official" and "approved", but you can't expect current and future writers to abide by all elements added for a comic tie-in that might only see a few thousand copies.
I've read it and seen the movie. Both are fun!
Those reading the comic may/will gain a few extra insights to the plot of the new movie. "Countdown to Darkness" (and "ST Ongoing") reveals easter eggs for the new movie, just as "Countdown", "Nero" and "Spock Reflections" did for the 2009 movie.