I am not entirely sure how comparable reputation and badges are across Stack Exchange sites. Of course, an obvious concern is that if the reputation points needed to earn certain privileges are uniform across Stack Exchange sites, then sites with a lower number of people will unambiguously be less conducive to mobility.
If this is indeed the case, should the reputation points needed to ascend to a new privilege not be scaled by number of users on the sites?
Reputation is an increasing function of likes, which are in turn an increasing function of number of users. If this is not already the case, this should be taken into account!
For instance, a 10,000 reputation on the Economics site implies much more of an 'impact' as regards the number of users on the site as opposed to, say 10,000 on Mathematics. My point is simple- a user on the 90th percentile in the reputation distribution should have the same privileges across sites.