How do you keep population numbers vague and still support lore about how industrialized the whole planet of Leeds are, the population density of the tower-cities of NT, the fact that Manhattan is supposed to be an ecunopolois? All of that leads me to lean toward large numbers. How vague do you want to leave that number? we could say "many" or "Few" or "sparsely populated"...but arguments like this aside (which I consider a feature, not a bug) I can't see what that would give us that the number do not, while numbers in the tens of billions are...pretty vague, honestly, given the scale of the number.
However, you're right about this being an art style choice, from the very lowest levels up. This is an imaginary world, and that leaves a lot of freedom up to us, the people who are imagining it. I think, to some degree, we ought have an idea of what those numbers are, and how they got to be that way, and where they're going, what sort of social and economic pressures they're causing, just for purposes of having a better fleshed out world to roleplay in, and furthermore, because that sort of information is very helpful to informing and developing stories, and the motivations of our characters.
I'm more or less okay with the population numbers that exist for planets right now. I think they're based on reasonable growth rates, which, as we've argued this way and that, you can niggle up or down and still be very reasonable. However, I think we could do with doubling, or tripling, the actuall number of people in Sirius, simply because the stations have populations in the hundreds and low thousands, which...Is that the world we're portraying?
I think, given the level of space based industry, the development of battleships and fleets at the level we see in vanilla, and project for our future, given, simply, the number of windows on larger ships, and that on stations, we could easily argue that there is headroom for many, many more persons on a station than 1000.