A full ride, $100K or thereabouts, is an awful lot of money to turn down, even more so in the current client.
The only X-factor I can see is your desire to work in Asia. I don't know how important that is to you. If you plan to work in Asia by being posted as an expatriate (i.e. work in a US firm then work your way up to a high level position in one of their Asian branches,) then I think you should still pick Haas.
However, if you plan to strike it out on Asia on your own, the Chicago name brand should be significantly more helpful. There are two big reasons for this. First, in many parts of Asia, "face" is very important, so reputation is extremely critical. While H/S/W are still the undisputed trinity, the remaining four M7 schools are also very well regarded even if they may not be so well known by the laymen. Second, the Chicago network in Asia should be much stronger compared to Haas. For example, Singapore has a ton of Chicago grads, and Korea's banking industry is also loaded with Chicago grads[0]. It should be significantly easier to find a position in Asia through your network if you went to Chicago.
In the end though, nothing will beat quality work experience at a top notch company.
[0] Wharton has the largest alumni base in Korea, Chicago is second but not by much.