There are many different kinds of Starbase and station, and often the same model is used in a way that shows it to be a different scale. The most obvious example of this is Spacedock: a Constitution Class nearly filled the doorway, although an Excelsior Class fit as well. When this model was used for a Starbase on TNG, the Galaxy Class Enterprise fit through the doors, despite being more than twice as wide as the Excelsior. This means the station was bigger.
There is almost no canon information on these stations, but lets see what we can rope in from non-canon.
Vanguard: Harbinger has a centerfold of the station: Vanguard, Starbase 47, is a Watchtower class station, with drydock facilities and stuff. It is 921 meters high and has 3 shifts of 800 each for a total crew of 2400, plus room for 1200 guests or 61500 in emergencies.
TOS-R used a version of this model scaled down to about 560 meters (according to Ex-Astris Scientia).
Ex-Astris Scientia also says that Starbase 375 isn't just a re-use of the Regula I lab, it has been scaled up to about 15 times original size (100m with the tanks becomes 750m without the tanks).
FASA, back when they did a roleplaying game for Star Trek, wrote up some stats for Regula I and K-7 and Spacedock. They said Regula I had a crew of 530, with room for 120 guests.(I think: my copy is fuzzy) That's whacked: no way that thing has more crew than the Enterprise.
Deep Space K-7 had a crew of 1130, plus 400 guests.
Spacedock had a crew of 101,145 plus 12,000 guests.
One other thing worth noting: between TOS and TNG, the number of crew per unit of volume went down dramatically. This is due partly, no doubt, to everybody getting bigger quarters, and probably the new systems need fewer crew to keep them running too. The result is that a TNG ship with the same volume as a TOS ship will have about 1/10 the crew. (Put another way, Voyager has about 3 1/2 times the volume of a Constitution Class, while the Galaxy Class is more like 25 times the volume.) So to get the crews of those stations in the TNG era, I'd start by dividing by 10 and start tinkering from there.
So, Starbase 84 looks just like Spacedock but is 2 1/2 times bigger. That means it has more than 15 times as much volume. Take the crew listed above, multiply by 15, divide by 10 for the improved tech, and I get about 158,000.
A Watchtower Class station in the TNG era would have a crew around 240, in three shifts of 80.
IMO,YMMV.
