I'm not sure it was explicitly shown to be off the main corridor (there was a cut between the two scenes) but one difference is clear - for the USS Constellation's AC room there is corridor access to that adjacent area (behind the mesh screens) which has the large computer consoles.
In TDM, a crewman just walks in there from the corridor. In TWTE, the external corridor shows no such door. Obviously the chief engineer of the Constellation got fed up of taking the long way round and inserted a door there![]()
There's more. In "I Mudd" we can see that the corridor outside the Aux Control Room door doesn't have the abrupt turn present in "The Way To Eden". This would suggest that the area outside of the AC was modified between Season 2 and 3 (or that the AC was relocated).