I'm not intimately familiar with the population studies of these people, but can speak a bit on populations in antiquity.

The overwhelming majority of it is just educated guesses/estimates. Very rarely do we get anything that states actual populations, and even those that did have censuses should be taken with a grain of salt.

So what do we look at? We look at the cities themselves mainly. We know that cities need to be able to house people, feed people, provide water, etc. So if we're only getting evidence of enough houses for 20,000 people, water (piped in or otherwise) for 30,000 people, etc. then we can start to doubt some of the higher limits.

However, we also can't just assume things were perfect either. We can't assume every room was a bedroom for one person. We can't assume that the amount of water would have been given to one person and used up (no excess) or that the amount of water was enough to give the right amount to all the people there (inadequate).

And so on and so forth. That is all to say that the reason we get such wide swings in population estimates is because different people are looking at different criteria and analysising them differently too. Some people may be very conservative, and go for the lowest, some may be a bit more open and go for the highest possible number.

So who's right? We usually will never know. Same thing happens with army sizes, with a lot of guesses -- though in antiquity this tends to go towards over-exaggerating rather than under, though there's probably a few instances of that happening too. Additionally, it's a common mistake to think that all members of an army lived in said place. Mercenaries were far more common than most people think, and this is fairly universal across antiquity.

/This is by no means describing the whole problem/study, there's a lot more factors to take into account, more areas of evidence we can look at (burials are fun), but just a very quick introduction.