Granted we don't know much about the crew compliment, but with all the extra components needed to operate as a battleship and in seperated flight mode, it's fairly obvious if you use common sense that the crew compliment would probably not be as high as an Intrepid class, which is indeed the same deck height. And as for supporting the hardware, well honestly much of it is automated so it doesn't need a large crew to operate. When we were first introduced to the Prometheus class, it was able to operate with a crew UNDER TEN. This is also why the Intrepid class doesn't have a larger crew compliment even though it's similar in size in terms of it's internal volume and space to a Constitution.
Some notes. Number of decks!=size. Length!=size. A Prometheus is about 20% larger than an Intrepid. An Intrepid is about 2.5 to 3 times larger than a Constitution, depending on whether one is referring to the original or the refit. That there has been increased automation over the years from TOS to VOY is pretty obvious.
On the other hand, it probably doesn't do well to trumpet that we saw Prometheus flown by a handful. Any ship can be flown by a handful. The question is if that is enough when things start happening... like battle damage. Only a handful in Starfleet may have been trained to use Prometheus, but I wager that the ship's intended crew is a whole lot larger. Not to say that they couldn't build a ship that self-repaired in a big way all by itself without needing biological crew at their tech level, but let's face it: that's not the Star Trek way, for better or worse.
As a tid bit, if Prometheus was to have the same crew density as Defiant, that'd turn into a crew of like 500.
On a related note ... I wonder what would be the maximum capacity of crewmen that Voyager can house.
If the Sovereign class which is 9 decks larger (11 as of Nemesis) is able to house about 800 (which might or may not be a standard crew compliment for that class), would it be a stretch to think an Intrepid would be able to house about a 500 people at max?
I mean ... if the Galaxy class is able to house about 10 000 people at it's fullest, then up to 500 for the Intrepid might be doable.
A Galaxy is 2 times larger than a Sovereign, which in turn is something like 3.5 to 4 times larger than an Intrepid. I would not be at all surprised if a Sovereign's normal crew complement is less than 550.