Just saw it again (saw it on Monday with my son in IMAX 3D--regular 2D showing this time, and I liked it better that way).
I like all the Trek movies (even the "bad" ones), though not all equally of course. I've seen every Trek episode and movie multiple times (been watching since 1973). Now that my bona fides are established (oh and I'm a few weeks shy of 49--seems to be a new requirement

), here are my thoughts.
One--I agree with all the comments about the film being the closest to TOS of the new cast--I'd say it's the closest, period (no longer rookies, in their prime, etc.). For anyone looking for the TOS "feel", this one is the closest.
Two--that said, I still like STiD a touch more (just watched it yesterday--needed to watch something to put my new home cinema projector to the test. Was planning to watch a few scenes to help assess my calibration of the settings, ended up watching the whole thing). Don't have a lengthy, detailed argument to offer. I simply preferred the story. To me, it seems grander in scale. But, YMMV.
Three--I still prefer the uniforms from the previous two films. Not a big point (and the ones Chekov and Kirk wear in Beyond are fine--don't like the standard Beyond uniforms).
Four--also, I prefer the score of STiD to Beyond. Maybe that has an influence on my preference.
Still enjoyed Beyond very much (as I have all the new cast films). Hope to see many more with this crew (without Yelchin, obviously--and sadly).