If it's going to be one area that a shipyard will keep up to date, it's the energy production and control facilities. Therefore, a standard model XVII-b Engine Room would have one of the principal upgrades that the Constellation got when she was retrofitted to Enterprise-style specs (that and a shiny new Bridge, presumably)In short, I don't believe all the Constitution Class ships were exact duplicates at all, at least on the inside.
...but it shared the 1701's modified, 2nd season engineering room. That is significant. I think that automatically sells the notion that the intent was that the Connies were the same internally, while the search for auxiliary control could be written off as the wrecked bulkheads / beams causing slight confusion. They did not spend too much time searching for the room, as it was in a familiar area.
Also, this is the first time (production-wise) that we saw the new version of the Engine Room. Whether you believe in a single Engine Room starship (that got a major makeover in the mid season hiatus) or a multiple Engine Room one (i.e. the other design was always there, we just never saw it during the first year), the fact is that we had never seen this variation of the space before, so its not a foregone conclusion to visually link this Engine Room to the Enterprise one.
As for Kirk almost missing Decker in the AC room, that may be due to a variation in layout (stemming from the Constellation's life as an earlier class or simply due to a later redesign by the ship's Engineer) or it may simply be that Kirk was on his way to the adjacent records room, where he later sends Scotty.
However, if AC is indeed on Deck 8 (as per the later episode I, Mudd) then that would place it in one of the smaller decks of the ship, so he wouldn't need to know exactly where AC was anyway - just "somewhere" on Deck 8.
Was the Constellation intended to be a carbon copy of the Enteprise? Quite possibly. However, original creative intent rarely makes it through unblemished to the final episode, especially when taken in context of the series as a whole. In this instance, there's not enough conclusive evidence either way.