It's only deeper because of that long neck, which has no actual livable space in it. Some space is made up by the saucer width, but not enough.
Even going with that, keep in mind that much of the hull of the Nimitz (below decks) is the hangar and maintenance area. And, of course, much of the aft of the ship is the nuclear reactor plants.
So, really, if the remainder of the ship can house, somewhat comfortably, 1200+ crewmen, I'm thinking the 400 of the Enterprise should be fine. As I said, the only issue would be a handful of the set-pieces, which chalk up to Hollywoodisms anyway.
Yeah, I don't really disagree with that, because that wasn't really my point. I was talking about the relative size/volume only.
Now, if you want to talk about the crew size, I'm sure you could fit 430 people into the ENT fairly easily, but it would probably require the 9 or 12 person-to-a-room set-up we saw in TUC. The TOS ENT is not built like they were trying to save space though. I mean...7 foot wide, 10 foot tall corridors all over for one.