how is it still that both these ships can be similar is size but be so different internally?
I would suggest a change in design philosophy between those eras: In TOS, the space between decks was thin, but there were entire decks packed with equipment and narrow maintenance access spaces, whereas in the TNG era a lot of that equipment is just sandwiched between the decks, accessed from above or below.
Also, there is room to doubt the 21 decks figure (which I believe originates from Mr.Scott's Guide to the Enterprise). Even if it got mentioned on-screen ... Didn't The Final Frontier give a number over 100, and numbered in the wrong direction?
As for the crew, advancing technology really can make a huge difference. It can be a bit hard to get real-world examples to help wrap one's head around that though, but I found two.
The Iowa Class Battleships, when introduced in the 1940s, had a crew of 2700. When they were refit in the 1980s, their new crew was 1800. That's a 33% reduction in the crew size due mostly to newer tech.
I believe I read that during the extensive refit of USS Enterprise 20 years ago (the nuclear aircraft carrier), they replaced its reactors with new units rather than just refueling. I recall reading that 5 new units could provide more power than the 8 old units, and each new unit was smaller than the old units. They were talking about how roomy Main Engineering was going to be after the refit because of that. The point here is, not only will new equipment need fewer guys to run it, it will be physically smaller too.
But wait, you say, if the equipment got smaller, why is the ship still huge? It's worse than you think: although their maximum dimensions are similar, the Interpid Class is actually about 3 times the size of a Constitution Class by volume. (
http://www.st-v-sw.net/STSWvolumetrics.html) So the crew is smaller, but the ship is
bigger.
One look at the crew quarters will help explain that: in the TNG era, ships are a lot roomier. Picard's quarters dwarf Kirk's.
Using the volumes from that site above, you see that the Constitution Class had about 490 cubic meters per member of the crew. The Galaxy Class, on the other hand, has about 5650, or roughly 10 times as much. And Voyager? About 4400, which is not quite as nice as a Galaxy Class, but loads better than an old Connie.
What's in that space besides bigger quarters? Holodecks and stuff. While the TOS hallways were pretty wide, by TMP they were pretty claustrophobic, but by TNG they were wide again (trivia fact: the TNG hallways use the same sets at the TWOK hallways, with the walls moved farther apart).
Don't feel too bad for those TOS crewmen, though: modern Coast Guard regulations for civilian ships only require each crewman have 30 square feet for his quarters.
