Let's see...
Yeah, the bumps are phasers. Two turrets to an emplacement on the saucer, plus four turrets on the bottom of the engineering hull and two above the hangar bay -- pretty much same as the TMP refit. Just the two forward-firing torpedo bays.
You already know how careless I am about how my ships fit into the "canon" Trek universe, so...I'd say this is a movie-era "new build", a modern vessel designed to similar specs and along the same mission requirements of the Constitution but different from the keel up. Probably designed about the time the Constitutions were being refit, with the notion that these could be the replacement vessels for that class -- the saucer hull is similar in contour to that of the Excelsior class, so there you go.
I don't know where the Carolina fits -- at this point it's a test-bed for me to practice a lot of modeling techniques.
The Phoenix is to the original Constitution more or less as this one is to the refit Constitution (I mean the NCC-800 Phoenix, not the NX-1800. I may yet go back and rebuild the old 1800).
I've just always been fonder of the ships of TOS and TMP than of the 24th century ones -- I like the size, for one thing, and the kind of detailing used in the TOS-based movies. These are among the reasons I'm so thrilled by the NX-01 on "Enterprise"; any new TOS-era ship is welcome where I'm concerned. Gotta love those nacelles Drexler put on that baby, and the glow-y lower sensor dome.